The Arkansas Legislative Council approved the resolution on Friday.
Republican Senator Jason Rapert of Conway is behind the measure that passed on a voice vote, despite Democratic opposition.
Rapert's resolution accuses Circuit Judge Chris Piazza of not upholding his oath to uphold the Arkansas Constitution.
Piazza set aside the state's gay-marriage ban in May. More than 500 same-sex couples were able to obtain marriage licenses before the state Supreme Court blocked the ruling pending an appeal.