After watching the movie The Unbelievers I got the impression that atheists are not accepted in the American Congress.
Are atheists allowed in the US Congress or not?
There is no ban on atheists in Congress; such a ban would violate the appropriately nicknamed No Religious Tests clause in Article Six of the US Constitution:
[...stuff about oaths of office...] but no religious test shall ever be required as a qualification to any office or public trust under the United States.
It would also violate the First Amendment, which bars the federal government from either promoting or requiring religion, and from messing with free exercise; requiring participation in any religious act is instantly illegal according to that as well (source: that's how "no religious tests" is enforced on states, via Fourteenth Amendment incorporation of the First Amendment).
In addition, as Geobits mentioned, Pete Stark is a US Congressman and a publicly declared atheist. Evidently, that didn't pose a legal barrier to his election.
That said: Atheists are highly likely to find it hard to get elected. Quite a lot of Americans wouldn't vote for an atheist on general principles; in 2012, a poll estimated it was around 43% for a presidential election, assuming the candidate was of their party and well-qualified. People are free to decide that atheists aren't suited, in their opinion, for elected office. You cannot stop people from deciding "I just don't trust someone who doesn't have the fear of God, so I won't vote for him" - the government is absolutely not allowed, under any circumstances, to prohibit you from voting however you please for whatever reason you want.
So, we would expect atheists to have trouble getting elected. In practice, an atheist is unlikely to be successful in an election in many areas of the US; this is largely a cultural thing, not due to the law. That's just how democracy rolls.