Grandparents Tax Credit Act of 2013 - Amends the Internal Revenue Code to allow grandparents of a minor child whose family adjusted gross income does not exceed 300% of the federal poverty level a refundable tax credit for up to $500 of the cost of household items (i.e., food, clothing, and other items typically used by or for the benefit of the child) paid for the benefit of such child in a taxable year.