Scaife, 31, was a sixth-round pick by the Tennessee Titans in 2005 and has 251 receptions for 2,383 yards and 12 touchdowns in his career. Scaife spent six seasons with the Titans, playing out 2009 on the franchise tag following his most productive season in the NFL (58 receptions, 561 yards, two touchdowns).
Scaife's production dipped to 36 catches for 318 yards after he was denied unrestricted free agency by the uncapped season in 2010, though he would set a career-high four touchdowns that season.
With younger tight ends Jared Cook and Craig Stevens emerging in Tennessee, Scaife was allowed to hit free agency after last year's lockout. Scaife was signed to a one-year, $1 million contract by the Cincinnati Bengals, but injured his shoulder in the preseason and was placed on injured reserve.
In addition to Carter, the Patriots have waived undrafted rookie tight end Nick Melillo and offensive tackle Jon Opperud, leaving them with two open spots on their 90-man roster.