Mix all of the dry ingredients together in a medium-sized mixing bowl. Beat in the egg and beer to form a thick batter.
Heat the oil in a medium-sized saucepan. When the oil has reached 350F, dip both sides of the apple rings into the batter, then carefully place into the hot oil. Cook each side for about 45 seconds or until golden brown and crispy.
Remove the rings from the oil and place onto cooling rack with a towel underneath to catch any dripping oil. Once cool to the touch, garnish the doughnuts with powdered sugar or drizzle with apple syrup.