Civil Justice Tax Fairness Act of 2013 - Amends the Internal Revenue Code to allow: (1) an exclusion from gross income for amounts received (whether by judgment or settlement, as lump sums or periodic payments) on account of 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.