In June 2018 a KC-135 was the oldest aircraft in inventory. It has since been retired I believe.
https://www.airforcemag.com/the-oldest-jet-in-the-air-force-refueling-bombers-on-the-frontline-in-the-pacific/
The airmen are flying KC-135R, tail number 57-1419, the oldest Stratotanker—and the oldest aircraft—currently in the Air Force’s fleet. The Block 40 variant of the refueler still doesn’t have modernized avionics unlike the rest of the fleet, but its mission capable rate is high, which is “pretty impressive,” given the operations tempo and environment in Guam, said Lt. Col. Nelson Perron, commander of the 506th Expeditionary Air Refueling Squadron.
The registration number is 57-1419 and it was manufactured and accepted into Air Force Service in 1957.