The Twins had designated Arcia for assignment June 17, making room for the return of utility player Danny Santana from the disabled list. With eight relief pitchers on the roster, manager Paul Molitor wanted more versatility on the bench.
Arcia appeared in 32 games this season, playing both corner outfield spots and batting .214 with four home runs and 12 RBIs, but the 25-year-old had only 11 at-bats this month.
The Rays, who play in Baltimore on Friday night, cleared room on the 40-man roster by designating right-handed pitcher Andrew Bellatti for assignment. The team will announce another move to open a spot on the active roster.
"He's put together some pretty good seasons," Tampa Bay manager Kevin Cash said. "He's shown some power in the past."
The Rays were in need of outfield help. They placed outfielders Steve Pearce (right hamstring) and Mikie Mahtook (broken left hand) on the 15-day disabled list earlier this week. Steven Souza Jr. and Brandon Guyer are also on the DL.
Arcia hit 20 homers in 372 at-bats in 2014. He is a .240 career hitter with 40 home runs and 120 RBIs over parts of four big league seasons.
Cash was Cleveland's bullpen coach when he saw Arcia playing for the Twins.
"He actually beat us up pretty good," Cash recalled. "So it's just another piece that we can maybe add and mix and match with. Hopefully a change of scenery will do him well and do us well in the meantime."
The Associated Press contributed to this report.