The Rangers made the moves on Wednesday in time for Saunders to start the night's game against the Minnesota Twins. Saunders left his only start this season on April 4 after getting hit in the left ankle with a line drive off the bat of Tampa Bay's Evan Longoria.
Saunders made four rehab starts, going 0-1 with a 3.80 ERA.
The 27-year-old Irwin has appeared in one career game in the majors. He had elbow surgery last season and spent the first two months of this season in Triple-A. The Rangers optioned Irwin and left-hander Aaron Poreda to Triple-A Round Rock.