Texas also sent catcher Carlos Corporan to Double-A Frisco on Wednesday for his second rehab assignment since spraining his left thumb in July.
The Padres designated Rearick for assignment Aug. 21. The 27-year-old made his major league debut for San Diego this season, allowing four runs in three innings over five appearances.
Corporan has been on the disabled list since July 17. His previous rehab assignment with Round Rock was cut short after four days on Aug. 3 because of additional discomfort with the injured thumb. He's hitting .178 with three homers and 15 RBIs in 33 games with the Rangers.