Preheat the oven to 350 degrees and grease a small bundt pan.
In a mixing bowl, combine the orange cake mix, instant vanilla pudding mix, 1/2 cup orange juice, vegetable oil, eggs, and 1 teaspoon vanilla extract. Stir until the batter is smooth.
Pour the batter into the prepared pan and smooth the top.
Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean.
While the cake cools in the pan for 10 minutes, whisk together the powdered sugar, 2 tablespoons orange juice, and 1/2 teaspoon vanilla extract to make the glaze.
Turn the cake out onto a plate and drizzle the glaze over the top while it is still slightly warm.