Dry the pineapple rings thoroughly on paper towels, patting both sides to remove all surface moisture.
Mix dry ingredients: whisk flour, sugar, baking powder, cinnamon, and salt in a bowl.
Add wet ingredients: egg, cold milk or sparkling water, and vanilla. Whisk to a smooth, pourable batter.
Heat oil in a deep pot to 365°F (185°C). Use a thermometer for accuracy.
Dip and fry: coat each ring in batter, let excess drip off, and lower gently into hot oil. Fry 2 to 3 minutes per side until deep golden brown.
Drain on paper towels and dust immediately with powdered or cinnamon sugar while still warm.