Can a us woman marry a man with a green card visa?

I presume from your question that the US woman is about to marry a man who is in the US on a Fiance visa. She can marry that person within 90 days of his entry into the US. Also the marriage should be a genuine one and not for the sake of getting a green card. If it is a fake arrangement, then the fiance may be deported back and the US citizen may face legal problems.