Can I join the U.S. Military even though I have a non-violent felony?

Back in 2003 I was sent to federal prison on a drug charge, I just finished my supervised release ( probation ) and I always wanted to join the military, the Navy to be precise. I took the asvab back in 2002 and scored a 73, but because of some poor choices I did not join. I’m 27 now, is it possible?