Can I become a u s citizen with a police record?

Possibly. It will depend upon more information about the police record including number of arrests, charges, number of convictions, statutes under which you were convicted, and sentence imposed. It would be best to have an experienced immigration attorney review your criminal history to determine eligibility. In the interim, you can read more about naturalization at http://myattorneyusa.com/how-to-get-naturalized-in-the-united-states.