If you are not convicted of a felony can you buy a gun?

Well, there's a lot of variables. The first being whether or not the case is dismissed or is still ongoing. If it's ongoing, you may not own, purchase, or possess a firearm.

The next question would be whether or not you were convicted of anything at all. Some misdemeanor charges will invalidate you from owning or possessing firearms (e.g., domestic violence).