Absolutely. The idea that men should be the ones to initiate dating is so passe. This is the 21st century. Woman are just as capable as men at anything, including initiating relationships.
Why in the world wouldn't that be okay. I don't really have any confidence left to ask a girl out, because I've never really had any luck the few times I have asked girls out. They usually end up being taken even though they had huge crushes on me.