Texas made the moves Thursday, when it recalled left-hander Ross from Round Rock to start that night in place of ailing Yu Darvish.
Darvish was placed on the 15-day disabled list Wednesday with right elbow inflammation. The Rangers had said then that Ross would start the series finale against Tampa Bay.
Adcock had a 4.50 ERA in seven relief appearances for the Rangers since getting called up July 24.
Converted reliever Ross began the season in the Texas rotation, and went 1-4 with a 4.78 ERA in nine starts before going back to the bullpen. He was optioned June 17 to Round Rock, where he started.