Texas announced the move Saturday, a day after Odor was a last-minute scratch from the starting lineup for the series opener against Oakland. Odor is expected to be re-evaluated in about two weeks.
The Rangers selected the contract of infielder/outfielder Danny Santana from Triple-A Nashville. Right-handed pitcher Edinson Volquez was transferred from the 10-day injured list to the 60-day injured list to create a spot on their 40-man roster.
Odor batted .167 with no homers and two RBIs in his 12 games this season.