Preheat oven to 350°F. Grease and line an 8-inch round cake pan with parchment.
Whisk flour, baking powder, and salt in a medium bowl; set aside.
In a large bowl, beat eggs and sugar until pale and slightly thick, about 2 minutes.
Mix in oil, yogurt, vanilla, and orange zest until smooth.
Stir in half the dry ingredients, then add the orange juice. Finish with remaining dry mix; do not overmix.
Scrape batter into the pan and smooth the top.
Bake until golden and a tester comes out clean, 38–42 minutes.
Cool 10 minutes in the pan, then turn out to a rack to cool slightly.
Whisk powdered sugar, orange juice, and zest until smooth and pourable.
Drizzle glaze over the warm cake. Let set 10 minutes before slicing.