The 28-year-old Scotland internationalist, who has also played for Partick Thistle and Luton Town, has penned a short-term deal at Fir Park until the January transfer window.
Manager Stephen Robinson told the club website: "He will give us greater options in both full-back areas, especially at a time where we are lighter on numbers due to injuries. He’s an international-level defender who will bring a lot to our squad."