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In a bowl, whisk the all-purpose flour with a pinch of salt; gradually whisk in the pale ale until completely smooth. Allow the batter to rest for at least 30 minutes or up to 1 hour.
In a large deep skillet, heat 3 inches of the vegetable oil to 370° over moderate heat. Stir the batter. Working in batches, dip the apple rings in the batter and fry them, turning occasionally, until golden and crisp, about 6 minutes.
Using a slotted spoon or a wire skimmer, transfer the beignets to a baking sheet lined with paper towels to drain. Keep the cooked beignets warm in a low oven while frying the rest. Sprinkle the beignets with granulated sugar or sift confectioners' sugar over them and serve hot.