School Principal Recruitment and Training Act of 2013

School Principal Recruitment and Training Act of 2013 - Amends the Elementary and Secondary Education Act of 1965 to establish a principal recruitment and training grant program awarding renewable, matching grants to states, local educational agencies (LEAs), and states and LEAs that partner with each other or with nonprofit organizations or institutions of higher education to recruit, prepare, place, and support principals in eligible schools.

Defines "eligible schools" as high-need schools, persistently low-achieving schools, achievement gap schools, schools with middle grades that feed students to high schools with low graduation rates, and rural schools served by high-need LEAs.

Requires grantees to work with experts and stakeholders to develop, during the first year of a grant, a leadership training program for principals, mentors, and other school leaders that prepares and supports them in leading effective school reform efforts in persistently low-achieving schools.

Requires grantees to use the grants, after that first year, to: (1) implement their leadership training program; (2) ensure that their training program is informed, on an ongoing basis, by consultations with experts and stakeholders and by tracking the performance of program graduates; (3) select cohorts of experienced principals to lead school reform efforts in persistently low-achieving schools; (4) support and encourage interaction among principals who have completed the training program; and (5) disseminate information to principals, mentors, and other school leaders engaging in reform efforts in persistently low-achieving schools.

Makes grant renewal decisions dependent on the Secretary of Education's evaluation of the extent to which the principals recruited, prepared, placed, or supported by the grantee have improved school-level student outcomes in eligible schools.

Directs the Secretary to: (1) evaluate the programs funded by this Act, and (2) identify and disseminate research and best practices related to those programs.