Qualifying Renewable Chemical Production Tax Credit Act of 2013 - Amends the Internal Revenue Code to allow a business-related tax credit for the production of renewable chemicals. 

Defines "renewable chemical" as any chemical that is: (1) produced in the United States from renewable biomass; (2) sold or used by the taxpayer as polymers, plastics, or formulated products or for the production of polymers, plastics, or formulated products; and (3) not sold or used for the production of any food, feed, or fuel.  Exempts certain chemicals, including those with a biobased content of less than 25%.

Directs the Secretary of Agriculture to establish a five-year program to allocate credit amounts. Limits the total amount of allocable credits under such program to $500 million, with a limit of $25 million to any taxpayer in any taxable year.