Civil Justice Tax Fairness Act of 2013 - Amends the Internal Revenue Code to allow: (1) an exclusion from gross income for amounts received on account of a judgment or settlement resulting from a claim of unlawful discrimination, (2) income averaging for backpay and frontpay amounts received from such claims, and (3) an exemption from the alternative minimum tax (AMT) for any tax benefit resulting from the income averaging of amounts received from an unlawful discrimination claim.