Whisk flour, beer, garlic powder, salt, pepper, and cayenne pepper together in a bowl until batter is evenly mixed; cover bowl with plastic wrap and let sit at room temperature for 1 hour.

Wrap bacon around each onion ring and arrange on a plate; refrigerate.

Heat oil in a deep-fryer or large saucepan to 325 degrees F (165 degrees C).

Dip wrapped onion rings in batter, shaking off any excess. Place battered onion rings onto a plate while dipping the rest; do not stack.

Fry battered onion rings, working in batches, in the hot oil until browned, about 5 minutes per side. Transfer cooked onion rings to a paper towel-lined plate to drain.