Race to the Top Act of 2013 - Directs the Secretary of Education to award competitive grants to states and local educational agencies (LEAs) to implement reforms and innovations designed to improve educational outcomes significantly for all students and reduce achievement gaps significantly among specified student subgroups.

Requires each grant applicant to have a comprehensive and coherent plan for doing so that includes, if applicable:

• improving the effectiveness of teachers and school leaders and promoting their equitable distribution;
• strengthening the use of data to improve education;
• implementing internationally benchmarked, college- and career-ready elementary and secondary academic standards;
• turning around its lowest-performing schools;
• supporting, or coordinating with, early learning programs for high-need children from birth through third grade;
• assessing kindergarten students' readiness for school success; and
• creating or maintaining successful conditions for high-performing charter schools and other innovative, autonomous public schools.

Requires each grantee to establish performance measures that track its progress in implementing its plan and improving educational outcomes for students and specified student subgroups.

Gives grant priority to LEAs with the highest number or percentages of impoverished children and those that serve rural schools.

Requires each state grantee to use at least 50% of its grant for subgrants to LEAs that participate in its plan. Allows LEAs to receive a grant and subgrant for the same fiscal year.