The right-hander's first outing was highly encouraging. Griffin allowed just one hit and struck out three in three scoreless innings for the Ports on Tuesday.
It's not yet known how many Minor League starts Griffin will need before potentially joining the A's rotation, but he can spend up to only 30 days on a rehab assignment, so July 1 would be the latest date.
Griffin went 21-11 with a 3.60 ERA in a 47 starts for the A's from 2012-13.
Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.