Update (Jan 13)
The Washington Post's updated reporting noted that the intelligence FBI had gathered was shared with their "law enforcement partners", which includes the Capitol Police. This corroborates the initial reporting by ProPublica in my original answer below.
The head of the FBI’s Washington Field Office, Steven D’Antuono, told reporters on Friday that the agency did not have intelligence suggesting the pro-Trump rally would be anything more than a lawful demonstration. During a news conference Tuesday, held after The Post’s initial publication of this report, he said the alarming Jan. 5 intelligence document was shared “with all our law enforcement partners” through the joint terrorism task force, which includes the U.S. Capitol Police, the U.S. Park Police, D.C. police, and other federal and local agencies.
He suggested there was not a great deal for law enforcement to do with the information because the FBI at that time did not know who made the comments. “That was a thread on a message board that was not attributable to an individual person,” D’Antuono said Tuesday.
However, the former Capitol Police chief denied that he had received that intelligence from FBI. From the same WaPo article:
Steven Sund, who resigned as Capitol Police chief, said in an interview Tuesday that he never received nor was made aware of the FBI’s field bulletin, insisting he and others would have taken the warning seriously had it been shared.
“I did not have that information, nor was that information taken into consideration in our security planning,” Sund said.
Update (Jan 12)
Editor's note: Strikethroughs denote that the information is outdated, see above update.
The Washington Post is now reporting that the FBI office in Virginia had issued an "explicit internal warning" on the day before the riot. However, it's unclear if that information was shared with Capitol Police.
A day before rioters stormed Congress, an FBI office in Virginia issued an explicit internal warning that extremists were preparing to travel to Washington to commit violence and “war,” according to an internal document reviewed by The Washington Post that contradicts a senior official’s declaration the bureau had no intelligence indicating anyone at last week’s pro-Trump protest planned to do harm.
A situational information report approved for release the day before the U.S. Capitol riot painted a dire portrait of dangerous plans, including individuals sharing a map of the complex’s tunnels, and possible rally points for would-be conspirators to meet up in Kentucky, Pennsylvania, Massachusetts and South Carolina and head in groups to Washington.
[ ... ]
An FBI official familiar with the document said that within 45 minutes of learning about the alarming online conversation, the Norfolk FBI office wrote the report and shared it with others within the bureau. It was not immediately clear how many law enforcement agencies outside the FBI were told, but the information was briefed to FBI officials at the bureau’s Washington field office the day before the attack, this official said.
The official, who like others spoke on the condition of anonymity because they were not authorized to discuss ongoing investigations, added that the report was raw intelligence and at the time it was written the FBI did not know the identities of those making the online statements.
Original answer (Jan 8)
It appears to be yes. From reporting by ProPublica:
In the days leading up to the attack on the U.S. Capitol, the FBI received intelligence that extremists were planning violence as lawmakers gathered in Washington to certify the electoral victory of President-elect Joe Biden.
FBI officials managed to dissuade people in several places from their suspected plans, a senior FBI official said — but there was not enough evidence to issue arrest warrants.
“Prior to this event, the FBI obtained information about individuals who were planning on potentially traveling to the protests, individuals who were planning to engage in violence,” said the senior FBI official. “The FBI was able to discourage those individuals from traveling to D.C.”
Although the official did not describe the tactics used, it is not uncommon for the FBI to disrupt potential threats by warning suspected extremists, passing the word indirectly through informants or using local law enforcement to pursue suspects for lower-level offenses.
The FBI shared intelligence about potential threats with the Capitol Police, which has been part of the FBI-led Joint Terrorism Task Force in Washington since 1995. But for reasons that remain unclear, a much-criticized security deployment by the police was unable to prevent the storming of the Capitol on Wednesday.
(emphasis mine)
More information from AP News's reporting (which some news sources cited):
The Justice Department, FBI and other agencies began to monitor hotels, flights and social media for weeks and were expecting large crowds. Mayor Muriel Bowser had warned of impending violence for weeks, and businesses had closed in anticipation. She requested National Guard help from the Pentagon on Dec. 31, but the Capitol Police turned down the Jan. 3 offer from the Defense Department, according to Kenneth Rapuano, assistant defense secretary for homeland security.
“We asked more than once and the final return that we got on Sunday the 3rd was that they would not be asking DOD for assistance,” he said.
The Justice Department’s offer for FBI support as the protesters grew violent was rejected by the Capitol Police, according to the two people familiar with the matter. They were not authorized to publicly discuss the matter and spoke on condition of anonymity.
