The moves were made before Wednesday night's game against the New York Yankees.
Phil Klein was sent back to Round Rock after pitching in both games since his recall Monday. He gave up one unearned run over five innings.
Rodriguez was 6-4 with a 4.90 ERA in 17 appearances for Texas, the last two in relief after starting 15 games before the All-Star break. Rodriguez allowed seven runs in one inning of work Tuesday in a 21-6 loss to the Yankees.
The 36-year-old Rodriguez signed a minor league deal with Texas after being released by Atlanta at the end of spring training. He has a 97-98 record with a 4.10 ERA in 275 games for Houston (2005-12), Pittsburgh (2012-14) and Texas.