Despaigne will be recalled from Triple-A Salt Lake on Friday to start against the Rangers, Maria I. Guardado of MLB.com reports.
Despaigne, who was acquired from the Marlins in a trade earlier in the week, will join the Angels' rotation over the weekend with Tyler Skaggs (groin) and Nick Tropeano (shoulder) both on the shelf. The 31-year-old owns a 5.31 ERA through 20.1 big-league innings this season (all with the Marlins).