Same as Ken, I can only find the two: 12th Alabama *Infantry*, Co. D, and Talledega's Camp of Instruction. This is from Broadfoot's listings, which are directly from NARA's compiled service record microfilm.
That does *not* mean that he did not enlist with that artillery unit...just that no record of it survives with NARA.
I'll also note that an "R. Parsons" is shown Land's Company of Alabama Militia. I have no idea what that unit is.