To make room on the 25-man roster, infielder Reid Brignac was optioned to Triple-A Durham after Friday night's game.
Allen, 26, has played parts of four seasons in the Major Leagues with the D-backs and Athletics. He appeared happy to be joining the Rays on Saturday.
"It's obviously a great team to be around, a great clubhouse to be in from a perspective of just being here," Allen said. "... I'm happy to be here, in that way. I'm excited."
In 109 Major League games, Allen has a .205 batting average with 11 home runs, 38 RBIs, 40 walks and 133 strikeouts in 331 at-bats. In eight Minor League seasons, Allen accrued 142 home runs.
"I guess people know me for power, but I want to be more than that," Allen said. "Hopefully the guys here can turn me into a complete player."
Allen seemed pleased to be in the same clubhouse with power-hitting left-handed sluggers Luke Scott and Carlos Pena.
"I'm trying to take all I can from them," Allen said. "I met Carlos and told him I was going to be in his back pocket. ... It's going to be a good experience watching these guys play."
Rays manager Joe Maddon said he does not have a clear role for Allen yet.
"Obviously, he's got big power, maybe as a pinch-hitter," Maddon said. "The fact that there's a strikeout involved, maybe there's a three-run homer in there, too. I don't have anything clear. So far, the roles [on the team] have been going pretty well. But I don't like people to sit around too long, either. So I'll try to figure it out."
Maddon said he met Allen for the first time before Saturday night's game.
"And he dropped a 'Mr. Maddon' on me and I said, 'Come on,'" said Maddon with a smile. "Just like I heard, he's really a nice kid. He's outstanding. He is all of that. Big power like we're talking about, plays several positions. I'm just curious to see what it looks like because I have not really had a chance to see him play."