The only way I know of to accomplish this is to allow an account to go into collections (meaning it's closed). At some point when the account is sold to an outside agency they generally will allow you to settle your balance using a major credit card. (I know this from personal experience years ago...)
Since I don't think this is exactly what you're wanting to accomplish, the 'short answer' is no.
You can basically get the same effective by doing a balance transfer from another card, but there are usually fees involved with that.
