Combine flour, baking powder, and sugar; reserve 1/4 cup for dredging currants. Add butter and milk to remaining flour mixture, stirring until blended.
Dredge currants in reserved flour mixture; stir into dough.
Turn dough out onto a floured surface; roll to 1/2-inch thickness. Cut dough into rounds with a 1 3/4-inch cookie cutter. Place on greased baking sheets. Bake at 400° for 15 minutes or until lightly browned.