Weber's contract was selected from Triple-A Pawtucket on Monday.
Weber has a career 5.01 ERA in 73.2 major-league innings, and he maintains a 5.04 ERA through five starts for Pawtucket this season. He's up to replace David Price, who landed on the injured list Monday with elbow tendinitis. It's not clear if he'll be taking Price's rotation spot in addition to his roster spot, but Weber was on the same pitching schedule as Price and would be available to start Tuesday's game against the Orioles if the Red Sox want to go in that direction. The Red Sox have three off days in the next 11 days and can get by without a fifth starter for an extended period after Tuesday.