The Constitution Party would probably be eager to gain the support of a (now) nationally-known figure. The question is that if Moore thinks he has a political future, would he want to basically forfeit any chance of being elected by defecting to a third party?
I don't know that the Constitution Party would have him. They had the chance to nominate Alan Keyes a few years ago and passed on it. Moore has far more baggage.
I would not be surprised to see Moore as a TV regular on some "off brand" religious network. Not TBN, but one of the knock-off networks.