Strengthen and Unite Communities with Civics Education and English Development Act of 2013

Strengthen and Unite Communities with Civics Education and English Development Act of 2013 - Amends the Adult Education and Family Literacy Act (the Act) to allow state leadership activities grants to be used to provide technical assistance to faith and community-based organizations desiring grants under the Act.

Directs the National Institute for Literacy to: (1) disseminate information regarding integrated English literacy, U.S. history, and civics education programs; and (2) study the effectiveness of distance learning or self-study programs for English language learners. Makes integrated English literacy, U.S. history, and civics education programs eligible for assistance under the Secretary of Education's national leadership activities program.

Requires the Secretary to award grants to states for integrated English literacy, U.S. history, and civics education programs, with each state's grant amount tied to the size and growth of their recent immigrant population.

Amends the Act and the Elementary and Secondary Education Act of 1965 to replace references to individuals of limited English proficiency with references to English language learners.

Requires the Commissioner for Education Research of the National Center for Education Research to establish a national research and development center for adult education and literacy, or include adult education if a center for adult literacy has already been established.

Establishes the Presidential Award for Business Leadership in Promoting United States Citizenship to be awarded to companies and other organizations that make extraordinary efforts in assisting their employees and members to learn English and increase their understanding of U.S. history and civics.

Renames the Office of Citizenship within U.S. Citizenship and Immigration Services of the Department of Homeland Security the Office of Citizenship and Immigrant Integration (the Office). Includes among its functions furthering the integration of immigrants into this country. Permits the Office to accept donations in support of its activities.

Authorizes the Chief of the Office to provide grants to states to: (1) form State New American Councils to develop and implement comprehensive immigrant introduction plans and disseminate information pertaining to effective English acquisition and civics education programs; and (2) award subgrants, through such Councils, to local governments to assist them in integrating immigrants into communities pursuant to such plans.

Establishes a New Citizens Award program authorizing the President to present a medal to up to 10 new citizens per year who make an outstanding contribution to this country.