Peel onions; cut into 1/2-inch-thick slices, and separate into rings. Place rings in a large bowl of ice water; let stand 30 minutes. Drain on paper towels.
Combine flour and next 3 ingredients; stir well. Add beer and egg, stirring until thoroughly blended and smooth. Chill batter 15 minutes.
Dip onion rings into batter, coating both sides well. Pour oil to a depth of 2 to 3 inches in a Dutch oven; heat to 375°. Fry onion rings, a few at a time, 3 to 5 minutes or until golden on both sides. Drain well on paper towels. Serve immediately.