Preheat your oven to 350°F (175°C). Line a cupcake tin with cupcake liners or lightly grease it.
In a mixing bowl, combine the grated carrots, whole wheat flour, unsweetened applesauce, water, vegetable oil, and baking powder. Stir until well combined.
Divide the batter evenly among the cupcake liners, filling each about 2/3 full.
Bake in the preheated oven for approximately 20-25 minutes or until a toothpick inserted into the center of a cupcake comes out clean.
Remove the cupcakes from the oven and let them cool completely on a wire rack.