Can a renter recind a contract if they have made a deposit, but not moved in yet?

Have you signed a lease?

If you've signed a lease then you are obligated to pay the rent until the landlord finds a new tenant or until the end of the lease term, whichever comes first.

If you haven't signed a lease then you can back out of the deal but most likely the landlord will be entitled to keep your deposit since they took the apartment off the market.