Details may be confusing, but I mean to ask whether federal armed forces, including the military (Army, Navy, etc.) and policing/investigative organizations (FBI, Bureau of Prisons, the U.S. Marshals, the Bureau of Alcohol, Tobacco, Firearms and Explosives, Homeland Security Investigations, Customs and Border Protection and the Defense Department), have ever acted violently against civil movements.
Yes basically, even ignoring the Civil War etc., the Ohio Army National Guard shot and killed some students during the Kent State shootings in 1970.
Twenty-eight National Guard soldiers fired approximately 67 rounds over a period of 13 seconds, killing four students and wounding nine others.
The Ohio Army National Guard is part of the US Army reserves in a somewhat convoluted way that applies to many state national guards.
Ohio Army National Guard is a part of the Ohio National Guard and the Army National Guard of the United States Army. It is also a component of the organized militia of the state of Ohio [...]
The Army National Guard (ARNG), in conjunction with the Air National Guard, is an organized militia force and a federal military reserve force of the United States. They are simultaneously part of two different organizations, the Army National Guard of the several states, territories and the District of Columbia (also referred to as the Militia of the United States), and the Army National Guard of the United States, part of the United States National Guard.
As for the latter:
The United States National Guard is part of the reserve components of the United States Army and the United States Air Force. It is a military reserve force composed of National Guard military members or units of each state and the territories of Guam, the Virgin Islands, Puerto Rico, and the District of Columbia, for a total of 54 separate organizations. All members of the National Guard of the United States are also members of the Organized Militia of the United States as defined by 10 U.S.C. § 246. National Guard units are under the dual control of the state governments and the federal government.
So the Ohio Army National Guard basically has this dual status too.
(Edit:) However as a comment points out below:
That unit of the Ohio National Guard was at the time under the command of Governor Rhodes. Since it was still under the Governor's command, it had not been "called up", and was not at that time acting as a part of the US Army. – T.E.D.
Apparently Nixon had not invoked the Insurrection Act of 1807... unlike his predecessor Lyndon B. Johnson who did so on several occasions. And at least in one of those, during the 1967 Detroit riots, there were separate (rather than mass shooting) cases of the Guardsmen killing civilians (but also being shot at and wounded or even killed by them), e.g.
The National Guardsmen engaged in what they said were firefights with locals, resulting in the death of one Guardsman. Of the 12 people that troops shot and killed, only one was shot by a federal soldier.
A selection from the list of the civilian casualties during this riot, to give an idea of the nature of the incidents:
(Clifton Pryor, [race:] White, [age:] 23 July 24, 1967. Mistaken for a sniper while trying to keep sparks from a neighboring fire off the roof of his apartment building; shot by a National Guardsman.
(Tanya Blanding, Black, [age:] 4, July 26, 1967) Died as a result of gunfire from a National Guard tank stationed in front of her house. Guardsmen stated that they were responding to sniper fire from the second floor.
(Helen Hall, White, 51, July 26, 1967) Hall, a native of Illinois, was visiting Detroit on business and stayed at the Harlan House Motel. Hearing tanks rolling by, she peeked through the drape window to see what was going on. She was shot by National Guardsmen who mistook her as a sniper.
(George Tolbert, Black, 20 July 26, 1967) Killed as he ran past a National Guard checkpoint at Dunedin and LaSalle Streets, when a bullet fired by a Guardsman hit him.
(Roy Banks, Black, 46 July 27, 1967) Banks was a deaf-mute walking to a bus stop to go to work; he was shot by Guardsmen who mistook him for an escaping looter.
(Ernest Roquemore, Black, 19 July 28, 1967) Shot by an Army paratrooper and declared dead on arrival at Detroit General Hospital. The soldier had been aiming at another youth who was unharmed.
The last one seems to be the case of the "federal soldier" mentioned in the summary para. In these riots there was concerted state and federal response with armed forces; apparently the Guardsmen were also called in by the state rather than the federal government in this case too, but the paratroopers were called in by the latter:
Governor George W. Romney ordered the Michigan Army National Guard into Detroit to help end the disturbance. President Lyndon B. Johnson sent in the United States Army's 82nd and 101st Airborne Divisions.
(Aside: during the 1968 Baltimore riot the Guardsmen intially involved were eventually put under federal command in Task Force Baltimore. It's not clear however from Wikipedia if any of the 6 deaths reported during that riot involved anyone from Task Force Baltimore, except for one traffic accident in which the fatality was a soldier.)
The US Army was employed to evict the Bonus Army from their camps in Washington. In 1932 17,000 veterans and 26,000 others (largely family of the veterans) were camped in Washington D.C. to demand payment of the "Veteran's bonus" they believed they were due for their service in WWI and desperately needed due to the hardships of the Great Depression. The US Attorney General ordered the removal of all the camps. Washington DC police attempted to enforce the order, and two veterans were shot and killed by the police. President Hoover then ordered the US Army to clear the camps.
Tanks, cavalry, tear gas, and adamsite (a chemical inducing vomiting) were employed to clear the area, and then the camps and the belongings of the protestors were burnt. Several later notable generals were involved in the action. Douglas McArthur was in overall command, George Patton had command of the tanks. Dwight Eisenhower was an aide to McArthur and urged McArthur not to take a public role in the matter.
This doesn't answer the title question but does answer the wider context of "have ever acted violently against civil movements." in the body of the posting.
With such a broad definition of "US army", the answer is trivially true as shown by the FBI assassination of Fred Hampton. If we include military-like actions by the police, incidents like the bombing of a city block in Philadelphia might also count.
For the US army itself there are at least
Federal troops took actions against railroad employees in the Pullman strike. https://en.wikipedia.org/wiki/Pullman_Strike#Federal_intervention
Force movements of native Americans including the Trail of Tears https://en.wikipedia.org/wiki/Trail_of_Tears
Has the US army ever fired against its own population?
Day 5 – Sunday, May 3
Mayor Bradley assured the public that the crisis was, more or less, under control as areas became quiet. Later that night, Army National Guardsmen shot and killed a motorist who tried to run them over at a barrier.
In another incident, the LAPD and Marines intervened in a domestic dispute in Compton, in which the suspect held his wife and children hostage. As the officers approached, the suspect fired two shotgun rounds through the door, injuring some of the officers. One of the officers yelled to the Marines, "Cover me," as per law enforcement training to be prepared to fire upon if necessary. However, per their military training, the Marines mistook the wording as providing cover while utilizing firepower, resulting in a total of 200 rounds being sprayed into the house. Remarkably, neither the suspect nor the woman and children inside the house were harmed. [Emboldening added.]
Going back further in time the New York Draft Riots of 1863 come to my mind, in which several thousand federal troops where used to suppress the riot.
Im no expert on American History, but I wouldn't be surprised if there were quite some more examples to be found in the earlier past, considering that the riot police is a rather recent invention.
No one has mentioned the Bonus Marchers from 1932. Wikipedia has a pretty good article here. Having 17,000 WWI veterans on the Mall was uncomfortable to the government. I've heard that some were armed, but haven't seen any pictures. It has been suggested that the Bonus Army was a driving force behind the push for a prohibitive tax on full-auto guns, and short-barrelled rifles and shotguns.
It was during World War II, but U.S. military police used tear gas and live ammunition against American citizens in an incident at the Manzanar internment camp in December 1942.
After Hall's addresses to the crowd after 8 pm failed to break it up, he decided that force would be necessary. At around 9:30, he ordered tear gas fired into the crowd. In the ensuing chaos, the crowd aimed a car sans driver toward the police station, causing MPs to open fire on it. Two other MPs, Privates Ramon Cherubini and Tobe Moore, fired into the crowd on their own initiative.
When the dust had settled, one young man, 17-year-old James Ito of Los Angeles, had been killed by the gunfire; another, 21-year-old Jim Kanagawa of Tacoma, would die of injuries several days later. Nine others were shot but survived.