I receive a diversion for a felony, can I still go into a career in law enforcement?

I was 18 when i was arrested and finished the program when I was 19. It sounds worse then what really happened but it still happened. I completed everything without a problem and finished my diversion program. I am 22 now and am about to complete my schooling and was just wondering, nerves are getting the best of me. I have talked to several cops and my teachers who both were captains in major cities and they all said I would have to start out in a small department and work my way up but I should have no problem at getting my opportunity. But i was just curious at what you all would have to say.