Preheat the oven to 180°C/350°F/Gas mark 4
Sift together the flour, sugar, baking soda and salt. Gradually mix in the orange peel, oil, orange juice and the vanilla until well-blended.
Drop by teaspoonful onto greased cookie sheets about 2 inches apart. Bake for about 10 minutes, or until the edges of the cookies are golden brown. Cool on racks and store in an airtight container.