Bishop was claimed off waivers by the Giants on Monday, Alex Pavlovic of NBC Sports Bay Area reports.
Bishop was designated for assignment by the Mariners on Thursday, and he'll now report to Triple-A Sacramento going forward. Bishop appeared in eight games for Seattle earlier in the season and could return to the majors at some point in 2021. Right-hander Reyes Moronta was transferred to the 60-day injured list in a corresponding move.