Access to Quality Diabetes Education Act of 2013 - Amends title XVIII (Medicare) of the Social Security Act to recognize state-licensed or -registered certified diabetes educators or state-licensed or -registered health care professionals who specialize in teaching individuals with diabetes to develop the necessary skills and knowledge to manage the individual's diabetic condition and are certified as a diabetes educator by a recognized certifying body.

Directs the Comptroller General (GAO) to study the barriers that exist for Medicare beneficiaries with diabetes in accessing diabetes self-management training services under the Medicare program.

Requires the Director of the Agency for Health Care Research and Quality of the Department of Health and Human Services (HHS) to develop a series of recommendations on effective outreach methods to educate primary care physicians and other health care providers as well as the public about the benefits of diabetes self-management training.