Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Combine the orange juice, figs and raisins in a small microwave-safe bowl and microwave until hot, about 1 minute. Let sit until the dried fruit is soft, about 10 minutes.
Transfer 1 tablespoon of the juice to a food processor, then drain the dried fruit and add to the processor. Add the honey, orange zest, lemon zest and cinnamon and pulse to make a paste.
Roll out 1 piece of dough into a 10-inch round on a lightly floured surface. Cut out circles using a 2 1/2-inch cookie cutter. Drop 1 teaspoon of the dried fruit paste in the center of each circle; fold the dough over to form a half-moon shape, pinching the edges together to seal. Crimp the edges with a fork, then poke a few small holes in the top of each. Repeat with the remaining dough and filling.
Transfer the turnovers to the prepared baking sheets; bake, switching the pans halfway through, until golden brown, 15 to 20 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely. Dust with confectioners' sugar.