The 29-year-old was looking for a club after being released by Doncaster last month following a short spell where he made nine appearances.
Manager Kenny Shiels said: "Sammy is a really good player. He passes the ball well, gets into good positions and knows the game so he is one we need badly."
Clingan, who has 33 caps, started his career with Wolves before playing for Chesterfield, Nottingham Forest, Norwich and Coventry.
He is eligible for Wednesday night's Scottish Premier League clash at Celtic Park, although he is short of match fitness.