Preheat the oven to 350 degrees. Butter a nine-inch round cake pan; line with parchment paper and butter this as well.
Combine the yogurt, 1 cup of granulated sugar, and eggs in a medium mixing bowl till well-combined. Add the flour, baking powder, and tangerine zest and stir until just combined. Add the oil and stir to make a smooth batter (this will take a couple of minutes). Pour into prepared pan and bake for 30-35 minutes or until a toothpick inserted in the center comes out clean. Remove from oven and invert onto a plate.
While the cake is still warm, combine the 1/3 cup of juice with the remaining 2 tbsp sugar and stir over medium-low heat until the sugar is dissolved. Poke holes in the cake and pour the syrup over. Allow to cool completely.
When the cake is cool, whisk together the confectioner's sugar and remaining 2 tbsp juice. Pour the glaze over the cake. You can serve immediately or allow the glaze to set up before serving.