This came up in another forum I frequent a few years ago, so we did some research. As best we can figure*, he's the Assistant Director in Charge of the Criminal Investigation Division. This means that there are three people above him in the chain of command: Executive Assistant Director (covers 5 divisions including Skinner's), the Deputy director, and the Director.
It also appears that his position is about as far as you go without playing heavy politics.
* Most FBI offices are run by a Special Agent in Charge, but Los Angeles, New York, and DC are run by Assistant Directors. It's POSSIBLE he's the AD in charge of the DC office, but given the things we've seen him have agents do that weren't X-Files related, this seems less likely.
Of course, all this assumes that Carter actually paid any attention to the chain of command.