Yep. Well, I guess it depends on what you mean by "in Congress."
Nothing in the Constitution disqualifies a felon from serving in Congress. That doesn't mean he or she can avoid serving time in prison, but conviction doesn't necessarily mean expulsion.
The issue is currently in the news due to yesterday's guilty plea by Rep. Michael Grimm, whose constituents in Staten Island re-elected him by a wide margin this year despite a pending 20-count federal indictment. As you may recall, allegations of wrongdoing have been dogging Grimm for some time, irritating him sufficiently that he threatened a reporter who mentioned them in January. See "Good Reason to Kill #48: Asked Wrong Question After State of the Union," Lowering the Bar (Jan. 29, 2014). “I’ll break you in half. Like a boy,” Grimm said to the reporter, in addition to threatening to pitch him off a balcony. (Breaking boys in half is not among the charges against him, so I'm guessing that was just a figure of speech.) During the campaign, Grimm said he would resign if “unable to serve,” presumably meaning something like “not able to attend meetings or vote on legislation due to being incarcerated.” That is now a distinct possibility.
On December 23, Grimm pleaded guilty to one felony charge of tax fraud, and admitted in the accompanying statement of facts that he had also committed perjury and wire fraud, among other things. He said afterward that he would “absolutely not” resign because of the conviction, but whether he will resign if “unable to serve” remains to be seen. Prosecutors are seeking at least two years in prison, but it is not impossible that Grimm could get probation. Sentencing will not take place until June 8, 2015.
That means, of course, that Grimm could be lurking around Capitol Hill for about six months as a convicted-and-felonious-but-not-yet-sentenced member of Congress. And as he reiterated after the plea, “as long as I am able to serve I’m going to serve,” Mr. Grimm said. “As of right now, I’m still in a capacity to serve, and that’s exactly what I plan on doing.”
A protester who may or may not have been a Democrat held a sign nearby reading “Grimminal,” which even if politically motivated is still pretty funny.
Again, nothing in the Constitution prevents him from serving in Congress despite the conviction, or even "serving" by phoning it in from a bank of federal pay phones. The only requirements (Art. I, § 2) are that representatives must be at least 25 years old, “seven Years a Citizen of the United States,” and an “Inhabitant of that State in which he shall be chosen” when elected. Under Section 5, either house can “punish its Members for disorderly Behaviour,” but it takes a two-thirds vote to expel a member, a requirement that itself implies that neither conviction nor anything else, for that matter, is enough to boot someone automatically.
Under House of Representatives Rule XXIII(10), any member convicted of a crime for which a sentence of two years or more may be imposed—which would include the charge to which Grimm pleaded—"should refrain from participation" in committee business and "should refrain from voting" until and unless vindicated, pardoned, or reelected. Assuming the House enforces that (making "should" into "will"), and assuming that's constitutional, then Grimm’s district would effectively be unrepresented until November 2016.
If that sounds intolerable, though, we should probably remember two things: (1) it’s Staten Island, and (2) D.C. residents have been in a similar boat for a long time—their representative isn't a felon, but isn't allowed to vote because D.C. isn't a state. (I don't think that's okay, I'm just pointing it out.) Still, the quality of representation is probably better when your representative's calls aren’t coming from a federal correctional institution.
Grimm told reporters that the guilty plea represented the end of a “terrible chapter in my life,” but since he is still under investigation for possible campaign-finance violations, there could be another terrible chapter after that one.