Rodriguez will be in his second stint with the Rangers this season, but has yet to pitch in a game. He was also with the club from June 18-20 but did not appear during Texas' three-game sweep in Kansas City. He opened the season on the 60-day disabled list with right biceps tendinitis before being activated and optioned to Round Rock on May 29.
Rodriguez has gone 1-1 with a 1.93 ERA and two saves in 17 relief appearances with the Express. He last pitched on Monday against Colorado Springs.
Martin allowed a run in the 10th inning to take the loss in Wednesday's 5-4, 10-inning loss to the Astros. He is 1-2 with a 4.32 ERA in 28 relief outings for Texas this season. The first date he would be eligible to return is July 15.