James for a girl? Well, why not? This is one of the traditional male names most adoptable for girls -- it's already been used as a pet name for some Jamies, and is the name of groovy young actress/model James King.
The only real argument against using James for your daughter is that it's been so widely used for so long for boys, and is more fashionable today than it's been for a couple of decades. Do you want people to do a double-take every time they hear your little girl's name? If so, James might be the choice for you, but if not, keep looking.