Anderson cleared waivers and elected free agency Sunday.
The Rangers designated Anderson for assignment Thursday.
The Rangers selected Anderson's contract from Triple-A Round Rock on Saturday.
The Red Sox released Anderson on Thursday, Chris Cotillo of MassLive.com reports.
The Red Sox designated Anderson for assignment Sunday, Rob Bradford of WEEI.com reports.
Anderson made his most recent appearance as a reliever in Saturday's 3-1 loss to the Twins, covering two scoreless innings while giving up one hit and one walk and striking out one.
Anderson (0-1) took the loss Thursday against the Guardians, allowing five runs on three hits and three walks over 1.2 innings. He didn't record a strikeout.
Anderson is slated to start Thursday's game against the Guardians in Cleveland, Ian Browne of MLB.com reports.
Anderson signed a major-league contract with the Red Sox on Saturday, Chris Cotillo of The Springfield Republican reports.
The Pirates released Anderson on Saturday, Ari Alexander of KPRC 2 reports.