Tie off the anchor to a cleat, then remove the rode from the anchor. Let the rode all the way out (be sure it is tied off in the anchor locker) while backing away from it slowly. The line will slowly "unscrew" the kinks as you back up. When the rode stops rotating, take it back up with your windlass and resecure the anchor.
Similar Rx to Franks. I've taken my stiff seriously hockled rode and while underway in deep water and at at idle in forward (and no traffic around), stream the rode aft and over the transom. let it twist itself free of hockles and kinks. Give it 5-8 minutes or so and then bring it in while coiling or flakeing back into the anchor locker. Reattach the anchor.
Not knowing how your anchor is attached to the rode, keep the spliced eye in the rode, no spliced eye? Leave a small shackle tied on the end of the rode. Don't use this method if your rode has an unseized end.