Technically they never say, and I find the way that Brandon T. Jackson played the part really well. He had that witty nervousness to him. And it doesn't matter anyways, black or white he'll eat all your recycling.
In the book, Grover is depicted as a chubby, pale, redhead. I believe the movie had a black Grover because they either could not find the right actor for the role, thought the guy who played the part was the best, or simply just to have diversity. I think the guy who played him in the movie did it well, so I have no problems with the decision, but I think the movie could have been better.