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Winkler agreed to a minor-league contract with the Rangers on Wednesday that includes an invitation to major-league camp.
Winkler appeared in 47 games for the Cubs last season and had a 5.22 ERA, 1.56 WHIP and 40:30 K:BB over 39.2 innings before being released in August. The 32-year-old could earn a spot in the Rangers' Opening Day bullpen with a strong showing during spring training.
