Can a landlord use your monthly rent payment as a pet deposit?

No.

Your rent is your rent,

Now if you owe a deposit, you have not paid, the lease may say these have to be paid first, I know all of my rental contracts state that all money received will be used to pay late fees and other fees due before they are applied to the rent.

So what does your rental agreemet say.

Plus why was the pet deposit not paid up front ?