Teaching Health Center Reauthorization Act - Amends the Public Health Service Act to appropriate funds for FY2016-FY2020 for the program of payments to teaching health centers that operate graduate medical education programs. Allows funds that were unexpended at the end of a fiscal year to be used in subsequent fiscal years.

Requires the Secretary of Health and Human Services (HHS) to: (1) annually report a compilation of the data provided to the Secretary concerning residency training, and (2) establish a minimum per resident per year payment amount for all approved teaching health center graduate medical education positions under the program that is not less than the amount as of January 1, 2013, and ensure that not less than that amount is provided to all such programs for all approved positions.

Authorizes appropriations for FY2013-FY2020 for grants to teaching centers for the establishment of new accredited or expanded primary care residency programs.