Youth Corps Act of 2013 - Amends the Workforce Investment Act of 1998 to authorize the Secretary of Labor to make grants to eligible public or private nonprofit agencies or organizations to carry out Youth Corps programs that utilize the Youth Corps model to provide eligible youth age 16 through 24 with education and work readiness training to enable them to find employment in the economy of the 21st century, and instill in them a sense of civic engagement and environmental stewardship.

Defines "Youth Corps model" as a youth education and training program for which an eligible entity provides eligible youth, among other things, with stipended or paid work experience and basic and technical skills training leading to: (1) enrollment in postsecondary education or training, (2) attainment of an industry-recognized certification or credential, (3) meaningful employment in the economy of the 21st century, or (4) military service.