Stephens follows teammate Lloyd Isgrove – who signed for Peterborough at lunchtime – in departing the south coast on a temporary basis until 3rd May.
The 20-year-old is the captain of Saints’ Under-21 side, for whom he scored the winning goal against Manchester City at the Etihad Stadium earlier this week.
He now heads into League 1, where he made five appearances as a 16-year-old with his first club, Plymouth Argyle, prior to joining Saints in early 2011.
Stephens signed a new long-term contract last April to keep him at Southampton until 2017, and now leaves temporarily in search of regular football for the remainder of the season.
Executive Director Les Reed says Stephens will benefit from the game-time he will pick up with the Robins.
“Like Lloyd [Isgrove], an opportunity has arisen for Jack to extend his development in the short term at a club where he will be encouraged to play good football until the end of the season,” said Reed.
“Jack has trained regularly with our First Team and played in several cup games and friendlies, and this experience will do him good as a prelude to pre-season when he will be challenged again with us.”