The Rangers made the move Monday. They also put left-handed pitcher Derek Holland on the 60-day disabled list while he recovers from surgery on his left knee.
The 28-year-old Parrino played 14 games for Oakland last season. He also played in the majors with San Diego in 2011-12.
In 93 games in the majors, he's hit .186 with one homer and 11 RBIs.
Holland had arthroscopic surgery to repair torn cartilage behind his left knee on Jan. 10. He was hurt a few days earlier in a fall at his home.
Holland is eligible to return to the roster on May 29.