Preheat oven to 400 degrees F. Prepare a baking sheet by greasing it or using parchment paper.
In a large bowl combine the flour, sugar, baking powder, baking soda, salt orange zest, and cinnamon. Add the butter and cut in with a fork or a pastry cutter until the butter is completely worked into the flour mixture and forms a crumbly mixture.
In another bowl combine the egg (slightly beaten), shredded carrots, oranges, and milk. Add the wet mixture to the dry mixture and by hand combine the two until it forms a ball. Do not overwork the dough.
On a lightly floured surface form the dough into a 8 to 9-inch circle, cut into 8 wedges. Place each wedge on the prepared baking sheet. Bake in the preheated oven for 15 to 17 minutes or until lightly browned.
While the scones are cooling prepare the icing. Add the powdered sugar into a small bowl, gradually add the orange juice until you have the right consistency.
Drizzle the icing over the scones and serve.