Possibly. Was this a minor misdemeanor?
A minor misdemeanor marijuana conviction in Ohio should not on its own prevent you from owning a gun.
Right now, federal law still classifies marijuana as a Schedule I controlled substance, however, and your state’s attorney general says the state will follow federal law. If you have a medical marijuana card, you cannot purchase a gun.
I agree with adjusterjack that you should speak with an attorney in Ohio who has experience in gun rights and drug offenses. What you don’t want to do is lie on any application about your conviction as that can get your application tossed.