Preheat the oven to 375 degrees F (190 degrees C).
In a medium bowl, mix together the vegetable oil, sugar and eggs. Stir in yogurt and orange zest. Combine the flour and baking powder; stir into the mixture just until blended. Pour the batter into a greased 9-inch baking pan.
Bake in the preheated oven until a knife inserted into the center comes out clean, about 30 minutes. Poke holes in the cake with a knife, and pour the juice from the oranges over the cake slowly until it has all been absorbed.