Griffin has joined the Royals on-loan to the end of the season.
Royals manager Brian McDermott told the club's official website: "Andy is an experienced player at the top level.
"He was skipper at Stoke, and got promotion there, so he's got great pedigree. I felt we needed a right-back and he can play that role so I'm sure he's going to be a good signing for us.
"He's hungry and wants to play. He hasn't played for a while though and needs to kickstart his career because he wants to play for another five or six years I'm sure.
"Hopefully we can help him do that."