Americans Giving Care to Elders (AGE) Act of 2013 - Amends the Internal Revenue Code to allow caregivers a tax credit for up to $6,000 of the eldercare expenses incurred for their parents (or ancestors of such parents).

Amends the Older Americans Act of 1965 to: (1) increase and extend funding for the National Family Caregiver Support Program through FY2017, and (2) require the Secretary of Health and Human Services (HHS) to award a grant to or enter into a cooperative agreement with a public or private nonprofit entity to establish a National Resource Center on Family Caregiving to provide information on and support for family caregiver support programs.