You will have to look in the Civil War Records for Company A, 2nd Cavalry Regiment. The on-line record at Ancestry.com indicates that he enlisted on 30 Nov 1863. On 17 Jun 1864, he was transferred into a Regiment U.S. Veteran Reserve Corps. This could indicate that he had been wounded or was otherwise unable to do his duties.
From the Regimental History, the 2nd Regiment arrived in New Orleans during April 1864; Company A was sent to Alexandria, LA. The record of battles fought by the 2nd Cavalry indicates that on 21 July 1864, they were engaged in operations near Berwick, LA.
There is a Rackliffe connection in my family, so I'm glad to be of help.