Cora, 34, has spent the last two seasons with the New York Mets after signing with the club as a free agent in 2009. He appeared in 62 games for the Mets this season, batting .207 with 20 RBIs, before he was released on Aug. 7. He missed the second half of the 2009 season after undergoing surgery to repair torn ligaments in both thumbs.
The 13-year veteran has a career average of .244 with the Los Angeles Dodgers, Cleveland Indians, Boston Red Sox and Mets. He appeared in 13 postseason games in his career, including two games in the Red Sox's four-game sweep of Colorado in the 2007 World Series.
He is expected to join Triple-A Oklahoma City for Wednesday's home game against Reno.
Manager Ron Washington expressed frustration with Arias over two missed defensive opportunities in the eighth inning that allowed the Rays to rally against Cliff Lee.