Special Counsel Integrity Act This bill sets forth requirements and limitations with respect to the discipline or removal from office of a special counsel appointed under Department of Justice (DOJ) regulations. Specifically, a special counsel may be disciplined or removed only by the personal action of an Attorney General who has been confirmed by the Senate. If the Attorney General is recused from the matter, then a special counsel may be disciplined or removed by the most senior DOJ official who has been confirmed by the Senate and is not recused from the matter. A special counsel: (1) may only be removed for misconduct, dereliction of duty, incapacity, conflict of interest, or other good cause, including violation of DOJ policies; (2) must be informed in writing of the specific reason for the removal; and (3) may file an action for judicial review of the removal.