The BFG 9000 is a classic weapon from the DOOM series, but it's also possible to obtain this in Rage 2. However, it's only available to players who have the Delux Edition of the game at this point in time, so you will need to buy this version to get the BFG 9000 weapon.
If you do have the Delux Edition, what you need to do is to log in with your Bethesda Account by signing in at the main menu in Rage 2. If you don't have one, don't worry, you can easily create a new account from the same menu. Anyway, when you have successfully logged in, just quit the game and reboot it. Now load your save game (or start a new save file), and you will get a quest with instructions on how to get the BFG 9000.
The quest will tell you to find a meteor that landed just outside of Vineland, so go there and look for it. Once you find the meteor, open it by shooting at it, and you will soon see the BFG 9000 inside it. Loot it, and it is yours to use for the rest of the game!
And that's how you get the BFG 9000 in Rage 2. There is currently no method to getting this weapon without owning the Delux Edition of the game, so you will have to shell out real money to upgrade your version to get this.