Texas brought back Klein before its series opener Monday against the AL East-leading New York Yankees. In two previous stints with the Rangers, Klein had an 8.25 ERA in eight games.
Right-hander Anthony Bass, whose 51 2/3 relief innings were third-most in the majors, was sent to Round Rock after back-to-back appearances Saturday and Sunday.
Right-hander Ross Ohlendorf was designated for assignment after 10 relief appearances during an injury rehab assignment at Round Rock. He was 1-0 with a save and a 3.52 ERA in eight games for Texas before going on the disabled list June 7 with a right groin strain.