There should be a threaded hole on the bottom of the ring for a set screw. But the screw is probably gone.

Replace the hardware. $45 at any big box home improvement depot.

Edit: Now I see the other picture. Blast off and nuke the door from orbit. Holy hell! I'm angry for you. Do what the other commenter said, re-bore the hole. You'll need to buy a jig and a proper sized bit.