.22WRF (NOT RF 22Magnum) is the correct ammo for the rifle as Mike states.
Remington called the round the '22 Remington Special',,Winchester labled it the Winchester .22 WRF.
One used flat tipped bullets,,the other pointed bullets and I can't recall which used what now but the case is identicle.
The 22 Remington AutoLoading Rimfire round was made and chambered for the Remington Model 16
Winchester had it's own odd stepchild semiauto round, the Winchester .22 Automatic, for the Model 1903.
Neither of these 2 autoloading rounds are interchangable with each other though the slightly smaller and straight cased Remington 22 Autoloader will chamber in the Winchester M1903.
The result is usually split or swelled cases as the 1903 chamber is larger in diameter at the rear.
The Remington 22 Autoloader cartridge is a straight cased short version of the 22 Remington Special (22 WRF) so it can be chambered in the Rem 12C rifle.
I don't know if the shorter case will work correctly through the repeating feed mechanism of the 12C.
Either of the odd 22 auto loading rounds are harder to find and more expensive than .22WRF anyway.
Look around for some of the recent limited production .22WRF ammo would be my suggestion for some occasional shooting.
I have heard of the chamber insert conversions being done to .22WRF rifles as described above to shoot .22LR ammo but never had any experience with them.
I'd probably leave a decent 12C alone and look for a nice pistolgrip/oct bbl 12 in 22lr to shoot. But an epoxyed insert is certainly reversable w/o harm if it doesn't work out if you want to try it.
My .02
