Improving the Juvenile Justice System for Girls Act of 2013 - Amends the Juvenile Justice and Delinquency Prevention Act of 1974 to include gender-responsive services in the grant program for juvenile delinquency prevention. Defines "gender-responsive services" to mean promising practices and evidence-based services that comprehensively address the needs of girls in the juvenile justice system by providing services that reflect an understanding of: (1) the unique pathways of girls into the juvenile justice system; (2) the need for interventions that address common experiences of girls in the system, including histories of abuse, violence, broken family relationships, and substance abuse; and (3) the social and cultural factors of girls in the system. Includes in such definition trauma-specific services. Authorizes appropriations for the Juvenile Justice and Delinquency Prevention Grant Program from FY2014-FY2019.