Harrison will be available in the bullpen for Saturday's game in Minnesota. He was placed on the disabled list May 12, retroactive to May 7, with left biceps tendinitis.
The right-hander, who opened the season as the fifth starter on the Rangers' rotaion, is 1-1 with a 5.29 ERA in six starts for Texas this season.
Harrison made two relief appearances on a rehab assignment with Double-A Frisco, allowing one run in 3.0 innings.
Moscoso was recalled on May 15 and made one appearance with Texas, allowing two runs in 2/3 of an inning May 20 against Baltimore. He has spent the rest of the season with Oklahoma City, going 2-2 with a 2.95 ERA in seven starts.
With Saturday's moves, the Rangers have 39 players on the club's 40-man roster.