Pre-heat oven to 350 degrees and line a muffin pan with baking cups.
Mix all dry ingredients together in one bowl and whisk all wet ingredients together in another bowl until frothy.
Add the wet ingredients to the dry ingredients and stir until mixed, then fold in the grated carrots and orange zest.
Pour the batter into the baking cups, filling them ¾ of the way full.
Bake for 25 minutes or until the tooth pick inserted in the center comes out clean.
Let the cupcakes cool completely.