Can a 21-year-old male get a contract for a 15-year-old girl to live with him?

no i think that's wrong and sick go find some one your own age.  

Answer

I am not sure I understand correctly, are you asking if you can become a 15 year old's gaurdian or if you can "live with" them in a relationship? I will assume it is the latter, and no, it is not allowed and you could end up in prison for statutory rape - be careful, and if you really love her, wait until she turns 18