Heat the olive oil in a deep, heavy-bottomed frying pan. In a large mixing bowl add the flour, salt, and water and whisk until smooth and even batter.
Drop large spoonfuls of the batter into the hot oil a few at a time. Let fry, turning as needed, until golden brown and crispy on both sides. Transfer to a paper-towel-lined plate to absorb the excess oil. Plate the fritters on a serving dish and sprinkle with icing sugar.