Peel and slice the onions into ½-inch thick rings and set aside.
In a large bowl, whisk the rice flour, tapioca flour, paprika, garlic powder, salt, black pepper, and cayenne pepper (if using) together.
Gradually add the chilled beer or carbonated water to the dry mixture, whisking continuously until you have a smooth, pourable, slightly thick batter. Adjust the liquid depending on the absorbency of your flour if needed.
Heat the oil to 350°F (177°C) in a large, heavy-bottomed pot, ensuring you use enough that it covers 2 inches of depth in the pan.
Working in batches, dredge each onion ring in the batter, ensuring it's evenly coated, and carefully drop the coated rings into the hot oil.
Fry until golden brown and crispy, about 2 minutes.
Drain on paper towels. Serve and enjoy.
Notes
Make sure the oil is heated to 350°F (177°C) before frying.
To bake: Bake in a 450°F (232°C) oven sprayed with oil for 15 minutes.
To air fry: Air fry in a 400°F (204°C) air fryer sprayed with oil for 10 minutes.
To store: Place leftover gluten-free onion rings in an airtight container in the refrigerator for up to 2 days.
To freeze: Store in an airtight container in the freezer for up to 3 months.