There's no reason why a girl can't ask a guy out. I'll give you the same advice I'd give to a guy, and that is to make it a smooth and easy part of a conversation. Don't make a big deal out of it because if you do, it can become awkward. Instead of asking 'Do you want to go out with me?' and forcing him to give a yes or no answer, make it easier for both of you.
Tell him you're planning to go somewhere or see some movie or you're trying to find someone to go ten-pin bowling with you ... and ask him if he'd like to come along. That's a much less difficult way for you to ask him out and give him the chance to say yes without feeling like it is an official 'date' (or say no without hurting your feelings too badly.)
After one or more of these casual get-togethers you'll know how you feel about each other. And after you've suggested the first one, he might suggest the next one.