Dear clever law chaps

I post a simple question that i hope someone maybe able to help me with, the US immigration websites are too complicated and unhelpful!

Can i (UK citizen) marry a US citizen in the USA, whilst working here as a scholar under a J-1 visa.

Is it necessary to apply for a fiance visa when i am already working here in the USA?

Any help to clarify this question would be greatly appreciated so i can plan with confidence my wedding.

thanks again for your help