The Yankees selected Bickford's contract from Triple-A Scranton/Wilkes-Barre on Sunday.
He'll join the 40-man roster and 26-man active roster as a replacement in the bullpen for right-hander Michael Tonkin, who was designated for assignment. Bickford had previously made five relief appearances for New York earlier this season and was hit hard over five innings, yielding eight earned runs on eight hits and one walk.