Can I join the U.S. Navy with a misdemeanor on my record?

About a year ago i was charged with a misdemeanor for possesion of marijuana. I do not smoke weed at all, and i was in a "friends" car when it happened. Being within arms reach of some pot, they charged me with possesion. I was recently turned away from the army because of this. I would like to know if the navy would accept someone like me with this on their record. As far as i know...the millitary was accepting felons a few years ago with waivers, and now the army is downsizing....