The 23-year-old joined Barrow at the start of the season from Stenhousemuir but made only six National League appearances for the Cumbrian side.
Murray began his career at Scottish club Motherwell and also had spells with Arbroath and Clyde.
Southport are 19th in the table, two points above the relegation zone.
Southport have signed defender Euan Murray from fellow National League club Barrow on a deal until the end of the season.