Moscoso has pitched just once since being called up to the Majors, hurling two-thirds of an inning against the Orioles on May 20, allowing two runs on two hits and two walks.
"We just haven't had the opportunity to pitch him," said Rangers manager Ron Washington. "We've been in some close ballgames and didn't have the opportunity."
Moscoso will go back to the Oklahoma City rotation. He was 2-2 with a 2.95 ERA in seven starts for the RedHawks before being called to the big leagues on May 15.
Harrison will return as a reliever. He made two appearances on medical rehabilitation assignment and allowed one run on three hits in three innings for Double-A Frisco. He walked none and struck out four.
The Rangers wanted Harrison to have one session with pitching coach Mike Maddux on Friday before activating him.