Norwood, 25, made his MLB debut with the Cubs in 2018, when he posted a 4.09 ERA in 11 relief appearances. He has a 4.95 ERA in 15 appearances at Triple-A this season.
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In a corresponding move, the Cubs optioned right-hander Rowan Wick to Triple-A. Wick allowed one run in one inning of work in the Cubs' 9-7 loss to the Phillies on Thursday afternoon.