Dillon's contract was selected from Triple-A Durham on Tuesday when shortstop Jason Bartlett was placed on the 15-day disabled list with a sprained left ankle. Dillon, 33, was Tampa Bay's designated hitter on Wednesday night against the Indians. The right-handed hitter can play second base, shortstop, third base and the corner outfield positions.
"I wanted to get him in there," manager Joe Maddon said. "I've heard he can handle left-handed pitching well and that's part of the reason why we brought him on board."
The Rays faced lefty Zach Jackson on Wednesday and are scheduled to go against left-hander David Huff in Thursday afternoon's game. Left-hander Francisco Liriano will start for the Twins Saturday.
"He's been around before," Maddon said. "It's not like it will be anything new to him."
Dillon was acquired from Oakland on May 9 as the player to be named later in the deal that sent infielder Adam Kennedy to the A's a day earlier.
Dillon arrived at Progressive Field during the fourth inning of Tuesday night's game. He missed the last month of Spring Training with a pinched nerve in his neck and started the season in extended spring training. He was on Triple-A Sacramento's roster, but had yet to appear in a game because of the injury at the time of the trade.
"That basically shut my Spring Training down," Dillon said. "I only had about half of a Spring Training."
Dillon appeared in 12 games with Durham, batting .262 with a homer and six RBIs. He's a career .257 hitter in the Majors, having also played with Florida in 2005 and Milwaukee in 2007-08.
"I've only been playing a couple of weeks," Dillon said. "I wanted to stay ready. You never know what's going to happen."
Steve Herrick is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.