Winn (0-1) was charged with Friday's loss after giving up four runs on four hits over a third of an inning against the Royals.
The Rangers recalled Winn from Triple-A Round Rock on Sunday.
Winn was optioned to Triple-A Round Rock on Sunday.
Winn allowed one run on two hits and a walk while striking out one over 1.2 innings in Monday's Cactus League start against the White Sox.
Winn has a 7.88 ERA and 2.00 WHIP in 16 innings for Triple-A Round Rock.
Winn was added to the Rangers' 40-man roster Tuesday.
Winn (ankle) will make his next scheduled start Sunday at Salt Lake, Kennedi Landry of MLB.com reports.
Winn struck out seven without a walk Tuesday for Triple-A Round Rock, but he only lasted 3.1 innings while allowing two runs on four hits.
Winn was promoted to Triple-A Round Rock on Thursday, Levi Weaver of The Athletic reports.
Winn (undisclosed) returned to Double-A Frisco's roster Saturday, Kennedi Landry of MLB.com reports