If you have an eviction on your record can you still get a lease if you have a co-signer?

Probably yes. It's really up to the apartmant management who they approve as renters. Some will want your co-signer with good credit to be the legal tenant, with you on the lease as another occupant. Then if you don't pay the rent, the co-signer is responsible. They also may be more flexible if you put up a larger deposit, an additional 1-2 months rent. Sometimes smaller apartment complexes or those owned by an individual will have less stringent guidelines.