Oakland will make a corresponding move before Friday's game against the Blue Jays.
Rosales was claimed by Texas on Friday and designated for assignment by the Rangers on Monday after not appearing in a game for them.
The infielder, initially designated for assignment by the A's after their acquisition of infielder Alberto Callaspo on July 31, is hitting .193 with four home runs and eight RBIs in 50 games with the A's this season.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.