IRS Equal Treatment Act of 2013 - Amends the Internal Revenue Code to: (1) require each officer and employee of the Internal Revenue Service (IRS) to substantiate any expense incurred in carrying out official duties and responsibilities, (2) make IRS officers and employees jointly and severally liable for all expenses for which substantiation requirements are not met, and (3) require the Inspector General for Tax Administration of the Department of the Treasury to report annually on a review of the expense substantiation records required by this Act.