Lorcan Halton, 45, from the Saracen area, was last seen in Cairnryan on Thursday January 9 where he boarded the ferry to Belfast.
Extensive enquiries are ongoing to trace him, however so far officers have been unsuccessful and are now asking for the public's assistance.
He is described as white, 6ft in height and of medium build with brown hair. He has a distinctive scar on his right arm. When he was last seen he was wearing dark-coloured jeans and shirt.
Detective Inspector Craig Willison of London Road Police Office said: "Mr Halton was due to attend court on January 15 but failed to appear and has not been seen since, although further enquiries revealed a sighting of him in Cairnryan on January 9 where he was boarding a ferry bound for Belfast.
"I would ask anyone who has seen Mr Halton, or who has any information regarding his whereabouts to contact Police Scotland.
"I would advise that no one approaches him, but rather contact police immediately."
Any information can be passed to Police Scotland on 101.
Alternatively contact Crimestoppers on 0800 555 111, where anonymity can be maintained.