While you can invite your overseas' girlfriend to visit you in the U.S., there is not a kind of visa straightly for boyfriend or girlfriend visit in the U.S. By sponsoring someone, that means you are petitioning a immigrant or non-immigrant visa for that person. If your girlfriend wants to visit you temporarily, she may apply for a tourist visa (B visa). However, if she intends to live with you on a more permanently basis in the United States, you may consider sponsoring her a fiancée visa (K1 visa).