Yes, he did. Thanks to the conveniently named precincts on the county clerk website, you can tell than Obama did in fact win Fayetteville. The reason Washington County went R was because of the suburban vote. Fayetteville went for Obama because it's home to the University of Arkansas, a major university.
He won it 52-43. Not much enthusiasm for either candidate, as turnout was only about 40% and third parties got 5%.
I think Gary Johnson managed to win a very sparsely populated precinct in the county that only cast one vote.