Border Security Tax Relief Act of 2013 - Amends the Internal Revenue Code to: (1) exclude from gross income, for income tax purposes, compensation received by a U.S. Border Patrol agent as administratively uncontrollable overtime pay (premium pay); (2) exempt such overtime pay from withholding of tax requirements; and (3) allow a taxpayer to elect to include such overtime pay as earned income for purposes of the earned income tax credit.