Hancock, 24, scattered two hits over two scoreless innings.
The sixth overall pick in the 2020 amateur draft, Hancock had yet to record a decision and owned a 5.40 ERA in two starts with Seattle.
He is no stranger to arm injuries, however. His start to last season was delayed by a lat strain.
Hancock posted an 11-5 record with a 4.32 ERA in 20 starts for Double-A Arkansas this season. He struck out 107 batters with 38 walks in 98 innings.