Can't use a centerfire rifle but you can use a rimfire.
I wouldn't recommend shooting a turkey in the body with a rimfire because you'll likely run out of ammo before it stops him, the only way to be sure with a rimfire is to head shoot them and since their heads are always moving it is best to keep the distances around 30 - 40 yards maximum. Basically the same range as a shotgun, so why bother, just use a shotgun. They are very smart birds and won't give you much time, it takes less time to line up on one with a shotgun then trying to lay a bead on him with a rimfire.
I have shot 2 turkeys with a .22 an one with a shotgun, I am going to try to use my bow this year since I hear the hardest thing to is draw on a turkey with a bow (unless your in a ground blind, which I don't have). If I wasn't using my bow then I'd be using my shotgun, no question about it.