Your ancestor's "capture" was a result of the surrender of the Confederate forces at Vicksburg on July 4, 1863. Here he along with the vast majority of the Confederate forces were Paroled. The enmasse surrender at Vicksburg almost paralyzed the Federal logistical system. U.S. Grant justified, and rightfully so, that he logistically could not feed, transport, and guard the surrendered forces of General Pemberton if he sent them in total to Northern Prison Camps. He felt that many of the parolees would desert or were in such poor condition they would be unable to return to duty.
The paper your ancestor signed was not an oath not to fight again but not to take up arms again "Until duly exchanged by the proper authorities." Please refer to the link below for a further information on how the exchange cartel worked.
His unit was "duly exchanged" around September 12, 1863, therefore, he was suppose to rendezvous back with his regiment at a designated parole camp. He was reported Absent without leave up to November 9, 1863 on the November, December 1863 Company Muster Roll. Not sure what his Sixth Georgia Cavalry records shows on a transfer. It was not uncommon for Vicksburg soldiers to go AWOL during this time period and it was not uncommon for them to seek service with Cavalry organizations during this time period and it was actually a real problem in the Confederacy.
I hope this helps.
Gerald D. Hodge, Jr.
War Between the States Historian
M.A. Military History - Civil War Concentration
Historian: 39th Georgia Volunteer Infantry Regiment