Well, all you have to do is make a bet with her that you can beat her on some game of your choice thats fun for the both of you. Preferably something that you know your good at. Place a bet that if she loses, she has to make you a sandwich. That way you get her to play AND she'll make you a sandwich when you beat her lol.
One thing I've noticed is that woman fall for WoW pretty easily. Two girls that my brother dated (still dating the second one) and a female friend he used to work with never played any of those types of games before. He got all three of them not only playing WoW but "hooked" on it. I dunno if its the social aspect of it or the casual gameplay or what but theres something about that game that attracts women to playing once they are exposed too it. Not saying every girl would get hooked but I find it pretty amazing to see three MMORPG beginners get hooked on WoW.