Police charged Caleb Moore, 24, with possession of a controlled substance and second-degree possession of marijuana after they responded to a report of an attempted break-in.
Officers said they found Moore nearby with four other men beside a pick-up truck. Police said they smelled marijuana, which they found in the truck's glove compartment. They also found Xanax pills and Moore's passport.
Moore, who was later released on $8,500 bond, blamed the arrest on the media and "crooked police officers."
"This is nothing more than a prime example of how media and crooked police officers and critics of my dad try to not only destroy his career for what he stands for but will go as far as trying to destroy his family," Moore wrote on Facebook. "I am not a drug user as the drug test taken today will show. As for the malicious possession charges, justice will be served."
Moore's father, Roy, recently made headlines for telling Alabama probate judges not to issue gay-marriage licenses shortly after a federal judge overturned the state's ban on same-sex marriage.