Chuck, there was no 22nd Arkansas (Colored) Infantry, and no Arkansas colored regiments at all in Confederate service.
The roster is undoubtedly that of Co. C, 35th Arkansas Infantry (redesignated as the 22nd Arkansas Infantry after the battle of Prairie Grove). Company C was a (white) Fort Smith company. Lieutenant William S. Birnie was a member of the company, who was later appointed regimental adjutant.
It sounds like a postwar document. I have no idea what it is worth.