I looked online and there isn't anything as far as a rocking chair swivel. There are swivel you can buy, but I think you would have to have someone make the large ring and cross supports and then mount it to a swivel.
Take a look at my photos - My Mods. There is one photo of the casters that I put on the OEM Flexsteel rocker, recliner, swivel chair.(I have to give credit to OZZ for the idea) You can see how the swivel attaches to the chair and how the ring/cross support attaches to the swivel. I think it would be cheaper and less frustrating to buy it from the manufacturer.
Another thought would be to try Goodwill or similar furniture store - buy chair cheap - take swivel off - donate chair back to them - declare the donation on your income tax.