Preheat oven to 400 degrees F (200 degrees C). Grease a baking sheet.
Stir the flour, baking soda, salt, and sugar together in a bowl, and cut in the shortening with a pastry cutter until the mixture looks like crumbs. Mix in the vegetable juice cocktail just until moist, and turn out onto a well-floured work surface. Gently knead several times just until dough holds together, roll out to 1/2-inch thick, and cut into rounds with a biscuit cutter. Place the biscuits onto the prepared baking sheet.
Bake in the preheated oven until risen and lightly browned, 8 to 10 minutes.