Clevenger replaced Ryan Lavarnway, who was designated for assignment.
Clevenger hit .352 with two homers and 14 RBIs in 27 games with Norfolk. He played in 35 games with Baltimore last year and in 118 major league games overall.
The seldom-used Lavarnway was batting .107 in 10 games.
Manager Buck Showalter said, "I just don't think Ryan's swing and the things that he's capable of doing are conducive to playing once a week."
Showalter hopes Lavarnway will accept a spot on the Norfolk roster.