Hello, I loaned my ex $480.00 over a period to help her out, but I did not ask her to sign anything. Also I asked her to move in with me, and at first I was paying all my bills at the apartment.

When we moved into a bigger apartment, we agreed to split the bills down the middle. She was never added to my lease, nor did I have her on the lease as an occupant.

Can I sue her for the loans and rent for one month without her signing anything?

The only thing I have is a text where she acknowledges the loan.

Oral agreements are binding. The text message, of course, verifies that there was an oral agreement. File in Small Claims Court - you will both give your version of events and the Court will believe one of you.