Hi Carmen,
Thanks for your question! The cheapest and most common way analysts use ArcGIS to do this work is to use the Districting for ArcGIS tool. This is a free-to-download extension for ArcMap which will provide you the basic capabilities you need.
If you are looking for more of an app feel, Esri Redistricting may be right for you. This is a hosted web app, integrated with ArcGIS Online that enables you to perform redistricting work and collaborate with others. This app is not free however- for pricing info, please contact redistricting@esri.com
Lots of other agencies have used such tools to do exactly the same work you need to do- If you do need help, I highly recommend the listserv of the International Association of Crime Analysts (www.iaca.net). The analysts on that board are always willing to help out with questions on method you might have!
Good luck, and feel free to contact me with any questions you might have!
Chris Delaney
Law Enforcement Patterns LeadEsri Law Enforcement Team