Can I report my roommate for theft if I gave her $600 to pay the rent but she in turn did not pay the rent?

You should file a police report and come up with the money to pay the rent that's due.

First find out why she did not pay the rent, tell that to the landlord, see if he is willing to just evict her, and then tell the police, but they probably will say it really is more of a minor civil matter and they can not and will not do anything about it.