Maybe consider slightly (and carefully) pinching down with wrapped plier pinchers at one or more locations on the mirror frame until the rotation stops?
Obviously use force carefully so not to fracture the glass.
I would stick tiny wooden shims (toothpicks?) in there between the glass and the frame at 12, 4 and 8, and trim to suit. You may or may not want to add a dab of adhesive with them. Try without first, see if it stays.
