Texas received Rosales on a waiver claim from Oakland on Monday, the second time that the veteran infielder has been acquired by the Rangers in the past 10 days.
During that time, Rosales also played one game for Oakland, which reclaimed him when he was designated for assignment by Texas on Aug. 5.
Rosales will report to Arlington on Tuesday and is expected to be used as an extra bench player.
This bizarre swapping of Rosales is happening with the Rangers and A's involved in a tight race for the American League West lead. The Rangers entered Monday with a one-game lead over the A's after trailing by six games on July 30.
"Adam is a quality big league infielder," Rangers general manager Jon Daniels said. "We've always liked the way he goes about the game, and the energy he brings. As our circumstances have changed over the past week or so, it changed our ability to carry him. We're glad to get a second chance at it."
Initially, Rosales was released by the A's, and the Rangers claimed him from their division rivals on Aug. 2 while Texas was in Oakland for a weekend series.
Rosales was active for three games but didn't play. He was designated for assignment on Aug. 5 to make room for Joey Butler, who was recalled when Nelson Cruz was suspended for 50 games for his involvement in the Biogenesis case.
Rosales was claimed back by Oakland on Thursday and played the following day at Toronto. He was designated for assignment by Oakland on Saturday.
Rosales, 30, is batting .191 with four home runs and eight RBIs in 51 games this season. The right-handed batter has played shortstop, second base, third base and left field this season.