That depends on the landlord/property manager. Since it's a hot rental market in DFW, many landlords are picky in selecting their tenants. If you must move and rent, you can tell the landlord your situation. Think also the answers to the following questions: Have you been paying your previous rent on time? Do you have any bills in collection? Any criminal record? How stable is your employment? How much do you make? You can offer the landlord double or triple deposit if you have the money and you have to move and rent.
I hope this helps!