If you are interested in renting from a rental complex than you shouldn't have much trouble although they may require an extra months security deposit etc.
If you are looking into leasing from an individual owner/landlord, you might have a bit more trouble as they have more risk. An individual owner does not have the same liquidity as a large corporation so they need to make sure they have a more financially stable tenant. They feel the hit more if there is an issue or late payments on rent.
Often times with residential leases you are required to submit an application fee with your rental application to the Real Estate agency. You might want to discuss your financial (bankruptcy) situation with the listing agent first so you are not waisting your money on an application fee only to find out that they reject you because of the bankruptcy when you could disclose that upfront.