Territorial TANF Equity Act of 2013 - Amends title XI of the Social Security Act (SSA) to remove the limitation on payments by the Secretary of Health and Human Services (HHS) to Puerto Rico, the Virgin Islands, Guam, and American Samoa under grants for assistance to the aged, the blind, and the permanently and totally disabled, including Supplemental Security Income (SSI) under SSA title XVI, as well as for Temporary Assistance for Needy Families (TANF) under SSA title IV part A and for foster care and adoption assistance under SSA title IV part E.

Replaces entitlement to a matching grant with entitlement to a supplemental grant for such territories of: (1) 10% of the payable family assistance grant to Puerto Rico, the Virgin Islands, and Guam; and (2) $100,000 to American Samoa.

Amends part A (Temporary Assistance for Needy Families) (TANF) of SSA title IV to make such territories: (1) eligible for the TANF Contingency Fund for State Welfare Programs, (2) Needy States if they satisfy alternative eligibility criteria established by the Secretary, and (3) eligible for child care entitlement funds. Prescribes a formula for allotment of child care entitlement funds to such territories.

Amends part E (Foster Care and Adoption Assistance) of SSA title IV to increase the federal medical assistance percentage (FMAP) for foster care and adoption assistance in such territories.