Preheat oven to 350 degrees. Lightly coat an 8-by-4-inch (1 quart) loaf pan with cooking spray. Set aside.
In a large bowl, whisk together sugar, oil, eggs, vanilla, and carrot juice. In a medium bowl, whisk together flour, ginger, baking powder, and salt. Add the flour mixture to the egg mixture, whisking just to combine. Fold in the walnuts.
Pour batter into prepared pan; bake until a toothpick inserted in the middle comes out clean, 45 to 55 minutes. Transfer to a wire rack; let cool in pan 10 minutes, then invert loaf onto rack to cool completely. Slice just before serving.