Veterans Education Counseling Act of 2013 - Modifies provisions relating to educational and vocational counseling for veterans to provide a program of counseling services to be known as the Academic Counseling and Educational Information Service. Requires the Secretary of Veterans Affairs (VA) to: (1) make available to veterans information about the definitions, eligibility requirements, and services provided by such counseling and how such counseling services differ from those provided as part of rehabilitation and readjustment assistance programs for veterans; and (2) maintain a website on which a person is able to request such counseling services.

Establishes as the primary goal of such counseling services to provide individuals with assistance in: (1) pursuing postsecondary education and training opportunities, (2) obtaining information about and data on such opportunities, (3) selecting a program of education or training, and (4) addressing other needs relating to education.