Farm Risk Abatement and Mitigation Election Act of 2013 or the FRAME Act of 2013 - Amends the Internal Revenue Code to: (1) establish tax-exempt farm risk management accounts (FRAME Accounts) and allow taxpayers actively engaged in the business of farming or ranching to use distributions from such accounts to protect the solvency of the farm to which the FRAME Account relates and to procure revenue or crop insurance; (2) allow a deduction from gross income for cash contributions to such accounts; (3) specify minimum levels of contributions to, and maximum levels of distributions from, such accounts; (4) set forth tax rules relating to account distributions, excess contributions, and prohibited transactions; and (5) allow a variable business-related tax credit for contributions made to a FRAME Account in the first nine years after such Account is established.