U.S. viewers can also catch it on the first episode of the seies The Finder on Fox TV the very same day. It's also the title tune for the series and John plays himself in the first episode.
In addition to Swamp Water he'll perform an acoustic version of Fortunate Son. That will also be available as a free download on his homepage, but just for one weeḱ.
UPDATE January 12:
Our mistake. Swamp Water is not available as a free download, but Fortunate Son is. Sorry for the misunderstanding.
In the episode John appears during the first six minutes of the show, getting his guitar stolen and back again and singing a shortened version of Fortunate Son before giving the hero his guitar pick and then exit.
Of the theme tune we get exactly 30 seconds. All instrumental with a couple of humming "yeeahs". Laidback typical swamp twang Fogerty groove. Should come with lyrics? Will be fun to hear the whole song eventually, Next album perhaps?
Anyway, here are the two free download links to the stripped down version of Fortunate Son that will work for seven days and no longer. Grab it while you can!: