If it is a KC-135, it is not a 707. It might look like a 707, but it is not. There are differences in fuselage width and other factors. The two programs, were developed at about the same time, with the C-135 having the Boeing model number 717 (not to be confused with the later MD-90 variant) with the Boeing 367-80 (pictured) being the common ancestor.

There are/were military 707 tankers, used by countries as diverse as Canada, Israel, and Iran, but none were in US service. (Note: there are photos of KE-3, derivative of the E-3 AWACS aircraft as part of a contract for Saudi Arabia, seen in USAF paint, but they were not really USAF aircraft.)