Early Intervention for Graduation Success Act of 2013 - Amends the Elementary and Secondary Education Act of 1965 to revise provisions concerning programs to reduce school dropout rates and increase school reentry and secondary school graduation rates. Replaces the existing grant program with an early intervention for graduation success program awarding competitive, renewable, five-year early intervention grants to states and, through them, subgrants to partnerships between local educational agencies and early childhood education providers that serve a high percentage of students who bear the risk factors for dropping out of school. Requires state grantees to: (1) create and periodically update a research-based plan that addresses the factors associated with the risk of not graduating from high school; (2) provide technical assistance to subgrantees; and (3) assist subgrantees in accessing data from appropriate state agencies to identify and direct effective services to children, from birth through elementary school, who are at risk of not graduating from high school. Permits states to use grant funds to: (1) provide tuition assistance to students who agree to teach in an early childhood education program, (2) increase and monitor the quality of early childhood education, (3) design and implement a progression of aligned performance standards across all domains of learning from prekindergarten through postsecondary education, and (4) expand access to high-quality early childhood education for children most at risk of low proficiency in school. Requires subgrantees to: (1) use the data relevant to risk factors for non-graduation a made available by state agencies and other sources to implement research-based, individualized interventions for at-risk students; (2) develop and implement individual learning plans for each at-risk early childhood, elementary, and secondary school student; (3) provide teacher training; (4) integrate community and family support services; and (5) foster students' high expectations and improve their chances for academic success. Authorizes appropriations for FY2014-FY2019.