Bring a large pot of lightly salted water to a boil. Slowly stir in the orzo and cook the pasta in boiling water until tender, 8 to 10 minutes. Drain the orzo and set aside.
In a large pot over medium heat, add the tomato juice, 3 1/2 cups water, salt and pepper and bring this to a boil. Reduce the heat and simmer for 10 minutes. Whisk in the sour cream, flour and egg and simmer for another 5 minutes. Stir in the cooked orzo and serve the soup warm with a dollop of sour cream on top.