Port Opportunity Reinvestment and Training Act of 2013 - Directs the Secretary of Transportation (DOT) to award renewable one-year grants to ports to provide summer jobs to high school students who live within each port's Metropolitan Statistical Area (MSA).
Requires the Secretary, when considering grant applications and amounts, to favor ports located in cities with high unemployment rates and also consider each port's cargo volume and the size of its MSA.
Allows ports to use the grants to provide job training to such students, provided no more than 15% of the students' time is spent training and they are compensated at their normal pay rate while training.