Morris was added to the Texans' 90-man roster, giving them four quarterbacks. Brandon Weeden and Joe Webb signed with the team as free agents this offseason and are expected to compete for the backup spot behind Deshaun Watson.
Watson is expected to be ready for training camp after missing much of last season with a torn ACL.
Morris, 25, has spent time with six teams since entering the league as an undrafted free agent in 2014. He has never played in a regular-season NFL game.