Commuter Parity Act of 2013 - Amends the Internal Revenue Code to modify the exclusion from gross income, for income tax purposes, of certain transportation benefits provided by an employer to an employee, to allow a monthly exclusion amount of: (1) $220 for transportation in a commuter highway vehicle from home to work and any transit pass, (2) $220 for qualified parking, and (3) $35 for qualified bicycle commuting reimbursement. Allows an annual cost-of-living adjustment to such exclusion amounts after 2014.