Rural Education Achievement Program Reauthorization Act of 2013

Rural Education Achievement Program Reauthorization Act of 2013 - Amends part B (Rural Education Initiative) of title VI of the Elementary and Secondary Education Act of 1965 to revise the Small, Rural School Achievement program, which gives rural local educational agencies (LEAs) federal formula grants and greater flexibility in the use of state educational funds.

Limits eligibility to LEAs whose schools are all designated with a school locale code of Fringe Rural, Distant Rural, or Remote Rural, unless located in an area the state defines as rural.

Raises federal grant limits when funds available to implement the program equal or exceed $100 million.

Alters LEA eligibility for federal funds under the Rural and Low-Income School program by requiring that: (1) at least 40% of the children ages 5 through 17 that LEAs serve be eligible for a free or reduced price lunch under the Richard B. Russell National School Lunch Act; and (2) all of their schools be designated with a school locale code of Distant Town, Remote Town, Fringe Rural, Distant Rural, or Remote Rural.