Combine the first 3 ingredients in a shallow baking dish; toss to combine. Weigh or lightly spoon rice flour and all-purpose flour into dry measuring cups; level with a knife. Combine flours and baking soda in a large bowl, stirring with a whisk. Gradually add beer, stirring with a whisk until smooth.
Heat a large skillet over medium-high heat. Add 3 tablespoons oil to pan; swirl to coat. Dip half of shrimp in batter; shake off excess. Dredge shrimp lightly in panko mixture. Place shrimp in a single layer in pan, and cook for 2 1/2 minutes on each side or until golden brown. Remove shrimp from pan; drain on paper towels. Repeat procedure with the remaining oil, shrimp, batter, and panko mixture.