Can you be police officer after completing diversion for a felony drug charge?

In short, yes. A diversion program allows for a person that would otherwise be convicted of a crime to have their charges dismissed if they complete the programs requirements. Assuming you completed the program and your charge was dismissed than you're not a convicted felon and may lawfully posess a firearm.

However, the morality of your crime may prevent you from being a police officer as this will be discovered in their internal hiring process.