Converting Methane Into Petroleum Act of 2013 - Amends the Internal Revenue Code to: (1) include in the tax credit for investment in a qualifying gasification project any qualified methane conversion technology, and (2) allow an alternative fuel excise tax credit for liquid fuel produced through qualified methane conversion technology at a facility the construction of which begins before October 1, 2024. Defines "qualified methane conversion technology" as a process for the molecular conversion of methane into hydrocarbons and the use of such hydrocarbons to replace or reduce the quantity of petroleum present in motor vehicle fuel and for the production of chemicals.