Set a wire rack on a baking sheet and place in an oven. Preheat the oven to 200°F. Line another baking sheet with paper towels.
Pour oil into a 7 1/2-quart deep fryer and heat over medium-high heat to 365°F according to the manufacturer’s instructions.
Put 1 cup of the flour in a pie dish or a wide, shallow bowl. In a large bowl, whisk together the remaining 2 1/2 cups flour, salt, onion powder and garlic powder until combined. Add the beer to the seasoned flour and whisk briskly until the batter is smooth.
Working with a few onion rings at a time, dust them with the flour, then dip them into the beer batter, letting the excess drip off. Using tongs, drop the onion rings, one at a time, into the oil and fry until golden underneath, about 2 minutes. Using a skimmer, turn the onion rings over and fry until golden on the other side, about 2 minutes more.
Transfer the onion rings to the paper towel-lined baking sheet to drain. Sprinkle with salt, then place on the rack-lined baking sheet in the oven for a few minutes. Repeat with the remaining onion rings, flour and batter.