Renewable Energy Construction and Investment Parity Act of 2013 - Amends the Internal Revenue Code to extend the energy tax credit to solar energy, fuel cell, microturbine, combined heat and power system, small wind energy, and thermal energy properties the construction of which begins before January 1, 2017. Requires amounts received from the sale of crude helium under the Helium Act to be deposited in the general fund of the Treasury to compensate for revenue lost resulting from this Act and to reduce the annual federal budget deficit or the public debt.