If I move in on the 15th, the landlord can only charge me for the part of the month I live there so it is prorated from the 15th to the 1st? If so, what is the law or statue or amendment that states this?

Depends on what your lease says, what state you live in, how much notice you gave and when your lease expires.

Some states don't allow pro-rating rent. Also, if you didn't give sufficient notice you may owe additional rental.

First I would assume you gave them notice on th 15th of last month, so they had at least a 30 day notice ?

Some require a 60 day notice.

I know in my rentals I never prorated any rents, and it is not common in the states I have lived.

So you need to read your rental paper work and talk to your landlord.

I am moving in, not out, its California, and I don't have the lease because I haven't moved anywhere yet.