Cueto elected free agency Monday.
The Angels designated Cueto for assignment Friday.
Cueto (0-2) took the loss against the Tigers on Tuesday, allowing six runs on six hits and one walk with five strikeouts over five innings.
Cueto (0-1) took the loss against the Royals on Wednesday, allowing three runs on eight hits and two walks over 6.1 innings while striking out one.
The Angels selected Cueto's contract from Triple-A Salt Lake on Wednesday.
The Angels will select Cueto's contract from Triple-A Salt Lake to start Wednesday's game against the Royals, Erica Weston of Bally Sports West reports.
Cueto had his contract selected by the Angels on Sunday, Hector Gomez of Z101Digital.com reports.
The Rangers released Cueto on Tuesday, Jon Heyman of the New York Post reports.
Cueto has agreed to push back the opt-out date of his minor-league contract with the Rangers to June 14, Ari Alexander of KPRC 2 in Houston reports.
Cueto signed a minor-league contract with the Rangers on Tuesday, Robert Murray of FanSided.com reports.