Air Traffic Control System Integrity Act of 2003 - Amends Federal transportation law to prohibit the Secretary of Transportation from authorizing the conversion to a private entity or a non-Federal public entity of any: (1) facility controlled by the Federal Aviation Administration (FAA) (except any airport traffic control tower operated under the contract tower program on the date of enactment of this Act); (2) operations performed, on the date of enactment of this Act, by Federal employees at an FAA-controlled facility (except any FAA airport traffic control tower operated under the contract tower program on the date of enactment of this Act); or (3) maintenance, engineering, or oversight functions performed, on or after the date of enactment of this Act, at an FAA-controlled facility (except with respect to renewal or replacement of a maintenance or engineering agreement in effect on the date of enactment of this Act).