Preheat the oven to 350°F (180°C). Grease a 9-inch (23 cm) cake pan or 9-by-13-inch (23 by 33 cm) baking pan with oil.
Fill a small saucepan with 2 to 3 inches (5 to 7.5 cm) of water and bring to a simmer over medium heat. Add the oil and rosemary to a heat-safe bowl and carefully set it over the saucepan. Keep the water at a low simmer and stir occasionally for 30 to 45 minutes to infuse the oil, then strain, let the oil cool, and store in a clean container until ready to use.
To a large bowl, add the aquafaba, clementine zest, clementine juice, and infused rosemary oil, then whip with a hand-held mixer on high speed for about 10 minutes, or until stiff, white peaks form. Add the cane sugar and continue whipping until the sugar dissolves and the peaks look glossy, about 5 minutes.
In a separate bowl, combine the gluten-free flour, arrowroot flour, baking soda, and a pinch of salt. Fold the dry ingredients into the wet and mix just until smooth.
Pour the batter into the prepared pan and bake for about 30 minutes, or until a toothpick inserted into the center comes out clean and the top is golden brown. Let the cake cool completely in the pan while preparing the glaze.
To make the orange glaze, in a small bowl, combine the powdered sugar, orange zest, and orange juice. Whisk until smooth and pourable but still thick enough to coat the back of a spoon. Add more orange juice, 1 teaspoon at a time, if the glaze is too thick, or more powdered sugar if too thin.
Drizzle or spread the glaze over the cooled cake and garnish with extra orange zest before serving.