Add the sugar to the freshly squeezed orange juice, stir, and let the mixture sit for 15 minutes so that the sugar dissolves. Stir again to ensure the sugar is well-incorporated.
Then, pour the orange juice into a wide, shallow, freezer-safe dish. Put the dish in the freezer. After 45 minutes, take the dish out of the freezer and stir it with a fork. Return the dish to the freezer.
After 30 minutes, take the dish out of the freezer and stir with the fork again before returning the dish to the freezer.
Continue freezing the granita, stirring it with a fork every 30 minutes, until completely frozen, about 3 to 4 hours total.