Soak onion rings in a bowl of ice water for 1 hour; drain and pat dry with paper towels.

Whisk flour, buttermilk, egg, baking soda, and salt together in a bowl until smooth.

Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).

Dip onion rings in batter, working in batches; fry battered onion rings in the hot oil until browned, about 5 minutes. Remove with a slotted spoon and drain on a paper towel-lined plate.