The 23-year-old, who joined the Bundesliga club from Melbourne Victory in 2013, has been loaned to Swiss Super League team Thun.
It's the second loan spell for the attacking midfielder who spent the first half of this season on loan to German second division club Greuther Furth.
He struggled for game time at Furth, playing just seven games.
Rojas's move to Thun was confirmed on the club's website and will be until the end of the season.
The Swiss league is in winter recess until early February, but Thun, which is fifth on the 10-team ladder, has practice games planned in January.
Rojas, who started his A-League career with Wellington Phoenix in 2009, is yet to appear in Stuttgart's first team.