How can I use a CyanogenMod theme with a stock rooted Galaxy S III? I'd like to make this my phone theme https://play.google.com/store/apps/details?id=com.ramazor.theme.freedea&amp;feature=more_from_developer

But it seems to require me changing my phone over to Cyanomod or something of the like. I'm not sure if I'm ready for that, but I do already have root access via SuperSU and was wondering if there might be another way to go about using this theme. 

I'm using a Samsung Galaxy S3 SGH-T999.
You cannot. The Cyanogen theming engine is specific to CM and derivative ROMs.

Samsung stock ROMs have Touchwiz UI, which is a proprietary layer. Theming CM to look like Touchwiz, or creating mashups would be easier because of CM's open nature. Some carriers might give packs, like Sprint (source).

You can install a different launcher and install themes on it, of course. Go Launcher, for one, has  many themes.