Yes they can. I have the perfect right to lease my apartment to anyone I wish, or deny leasing it to anyone I wish.
I encourage you to try.
I encourage you to then tell the authorities that the Fair Housing Act does not apply to you. Maybe you're ignorant and you really don't understand the concept, or maybe I'm wrong and you're in the extremely narrow minority of property owners that are exempt from the Fair Housing Act.
Go ahead and tell a Black, Hispanic or Jewish person that you will not rent to him based on race, ethnicity or religion.