Biff, I am not aware of what the laws in your state may say about this. The best option would be to consult with an attorney. It is well worth the investment. As for my understanding of gun ownership laws in general, I would say yes you can legally purchase and own a firearm. But again, I am not in your state. Some states require a permit to purchase and or own a firearm. My state does not.
And forget about what Daveyo said. You were "convicted" and I presume you have done your time or paid your fine. It's over with. It's time to move on.