Not to discourage you, but I'm not so sure that would work, assuming you mean to "scan" the user's fingerprint in order to ID them.
Obviously putting your finger on the screen will do nothing, and placing your finger directly on the camera lens would not work either as the camera would see nothing due to no ambient light.
Beyond that, most phone cameras cannot focus well at very close distances. At the closest range that it would focus, I doubt there'd be enough detail to tell one fingerprint from another.
If you mean taking exisiting images of prints and compare them looking for a match... well, I wouldn't really know where to begin but I suppose that could conceivably work. Although you may be better to have the processing done on a server somewhere rather than the phone. I know that technology does exist, but I would guess it's pretty complex stuff.