The move, which was first reported by CBS Sports, is figured to be a response to Delino DeShields leaving Sunday's game with a left hamstring injury. DeShields' status has not been released, but he was scheduled to undergo an MRI on Sunday evening.
Odor, who left Sunday's game with the Express after one at-bat, hit .355 with five home runs for Round Rock in 107 at-bats after hitting only .144 in 90 at-bats for the Rangers earlier this season.
The move likely means Joey Gallo will shift into left field and Hanser Alberto or Adam Rosales will take over at third with Adrian Beltre still recovering from a sprained left thumb.
Jake Smolinski replaced DeShields in Sunday's 4-3 loss to the Twins, but he is hitting .158 in 58 at-bats. Ryan Rua could also be an outfield option, but he is still finishing a Triple-A rehab assignment.
Cody Stavenhagen is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.