Trace my stolen iPhone through serial number

No, you can only potentially track it via Find iPhone (either via the app on another iOS device or http://www.icloud.com on a computer) if you had Settings > iCloud > Find iPhone enabled on the phone. I assume you've contacted the police and the carrier.

If it still has activation lock the police can potentially locate it.

Carriers can track any device on their networks using the IMEI. They will require a court order to do so, however. It's unlikely, unless someone's life is at risk, that they will pursue that action.