You can get married to anyone you want in the US. You just need to have some sort of id and be able to pay the license fee. My wife and I are both non-residents here, and we are in fact citizens of different countries, and we got married here. The US marriage certificate was recognized in our respective home countries, so we are legally married there too.
So no worries, they really don't care where you are from. They don't even care if you're here legally.
