Training Highly Skilled Americans Act of 2013 - Amends the Immigration and Nationality Act to establish in the Treasury the STEM Education and Training Account.
Requires employers to submit along with an application for a certification a $1,000 fee (to be deposited in the STEM Education and Training Account).
Sets aside specified amounts for: (1) a low-income STEM scholarship program, (2) K-12 STEM education, and (3) STEM capacity building at minority-serving institutions.
Authorizes grants to eligible entities for American Dream Accounts for a group of low-income students.