Yes, depending on the type of pet. There are many health benefits associated with the ownership of pets. Because of this, the federal government specifically provides that the elderly and disabled are permitted to keep pets in any public housing. A public housing landlord cannot discriminate against you because you have a pet nor is the manager or landlord of public housing allowed to prevent you from owning a pet. The pets that are covered by law are common household pets, such as dogs, cats, birds, rodents, fish, and turtles. Landlords, however, may prohibit you from keeping an exotic pet such as an iguana or a snake. Landlords may also impose reasonable regulations concerning common household pets.
See also our publication Tenants & Landlords: Rights and Responsibilities
For more information, see: 24 C.F.R. §§ 5.306, 5.309, 5.312, 5.315 (2015).