Supporting Community Schools Act of 2013 - Amends part A of title I of the Elementary and Secondary Education Act of 1965 (ESEA) to authorize local educational agencies (LEAs) to use school improvement funds to transform schools identified as needing improvement, corrective action, or restructuring into community schools. (Schools are identified as needing improvement, corrective action, or restructuring when they fail to make adequate yearly progress [AYP] toward state academic performance standards.)

Defines a "community school" as a public elementary or secondary school that partners with community-based entities, both public and private, to address students' academic, health, and developmental needs while also serving as a community center that provides or hosts relevant community services.

Requires such schools to be based on research into successful practices in: (1) improving student achievement or growth, (2) closing achievement gaps between groups of students, and (3) increasing student attendance and graduation rates.

Authorizes LEAs to use funds under part D (Prevention and Intervention Programs for Children and Youth Who Are Neglected, Delinquent, or At-Risk) of title I of the ESEA to fund a community school coordinator who will support their community schools.