Preheat the oven to 350°F. Grease two 9-inch round cake pans with butter or nonstick spray and dust with flour, tapping out any excess. Line the bottoms with parchment rounds. If you like, wrap the pans with bake-even strips according to the package directions.
In a large mixing bowl or the bowl of a stand mixer with the whisk attachment, whisk together the cake flour, granulated sugar, baking powder, and salt until well combined and no lumps remain.
With the mixer on low speed, add the oil, egg yolks, and orange juice. Increase the speed to medium and beat until the batter is smooth and slightly thickened, 2-3 minutes, scraping down the bowl as needed. Stir in the orange zest just until evenly distributed.
In a separate large, clean mixing bowl, add the cream of tartar to the egg whites.
Using a hand mixer or a clean stand mixer with the whisk attachment, beat on medium speed until foamy, then increase to high and beat until stiff, glossy peaks form, 3-5 minutes.
Using a spatula, fold one-third of the egg whites into the batter to lighten it, then gently fold in the remaining whites just until no visible streaks remain. Take care not to deflate the whites.
Divide the batter evenly between the 2 prepared cake pans and smooth the tops.
Bake until the tops are golden and a toothpick or cake tester inserted in the center comes out clean or with only few moist crumbs, 22-27 minutes.
Let the cakes cool in the pans on a wire rack for 10 minutes. Run a thin knife around the edges to loosen, then carefully invert onto the rack, peel off the parchment, and turn right-side up. Let cool completely before frosting, about 45-60 minutes.