Can I join the military with a drug arrest but no conviction?

I want to join the military however, two years ago I was arrested. I have never been arrested before. Although I was arrested and charged with the possession of Narcotics and tresping. I was not convicted. I have a clean record, however I was told from recruiters of different branches that I would not be able to sign up since I was arrested and charged, regardless if i was convicted. I have a BA, am a Nationally registered EMT, and Eagle scout. I was just in the wrong place at the wrong time. Does anyone have any advise for me?