The Rangers signed Barraclough to a minor-league contract Monday.
Barraclough -- who has been assigned to Triple-A Round Rock -- held a 12.91 ERA in three relief appearances with the Red Sox last season. The 33-year-old was used in the rotation last season at Triple-A Worcester, which was the first time he had been deployed as a starter on a regular basis in professional ball. It's not clear what role the Rangers have planned for him at Round Rock.