How can I marry a foreigner who is already living in the US for school with a visa?

It is not completely clear from your questions what your and your fiance's goals are. Generally, one may get a marriage license in Georgia and become married in Georgia when one of the spouses is here in a valid F-1 visa. It will be very difficult, however, for a foreign student to get a renewal of his F1 student visa or to re-enter the U.S. on an F1 visa if he is married to a U.S. citizen, since there may be a presumption that he intends to reside permanently in the U.S. and that is incompatible with an F1 visa. If you and he may be interested in your fiance may be interested in your fiance becoming a lawful permanent resident (getting a "Green Card"), there are multiple options for going forward, each with its pros and cons, and issues relating to timing. To address this in more detail, including review of eligibility issues, it would be wise to consult with an immigration attorney. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

You can marry whoever you like. You do not need to apply for him, but generally it is a good idea because it is hard to get a non immigrant visa for someone who is married to a US citizen.