In U.S. government parlance, the phrase "Foreign Agent" refers to anyone who is working for the interests of a government that is not the government of the United States, regardless of citizenship of person. Lobbies for other nations may represent U.S. Citizens interests in foreign policy with respect to that nation OR that nation's interests with respect to U.S. Foreign policy. While the latter is typically the job of an Ambassador and embassy staff, it's perfectly legal to go to lobby firms, which better know the ins and outs of Washington politics and may help the Ambassador do his or her job. The other common reference to "Foreign Agent" is typically a spy... which is technically true as they are acting on behalf of a foreign government... but it's not in any diplomatic interest.
In both examples, this usually requires a person who is a U.S. Person (typically a citizen, though a U.S. Resident may do) so to distinguish from legal lobby work and illegal espionage work, anyone in the U.S. working for a foreign government must disclose or register as such (Embassy staff typically don't, as there is a very different process that accredits the individual as an ambassador or other staffer). Naturally, spies do not register... at least the ones with a functioning brain, as registering as a spy makes the counter-intelligence agent's life a hell of a lot easier.
It's important to point out that a "Foreign Agent" need not be a "Foreign Citizen" nor is a "Foreign Citizen" necessarily a "Foreign Agent" a German working on a work Visa in the United States and working for a private industry, not the Government of Germany, and is thus not an Agent. Agent in U.S. terminology is "one who works for a government", typically with executive functions but not all government have three branches of government... or divided the same powers among them.
So it is entirely possible for a U.S. Citizen to be a Foreign Agent. Registering only discloses that you are taking money from a foreign government for work done on their behalf, not that you are switching to support them in violation of laws. If you apply for jobs with security clearances with the U.S. Government, it's not an automatic disqualification either, but you should probably not be surprised when you get a lot of questions about what you were doing when you were a foreign agent.