Preheat the oven to 325°F (165°C). Grease and flour a 9x13 inch baking tin or line it with parchment paper.
In a large bowl, whisk together the flour, sugar, baking powder and salt until well combined.
Add the eggs, oil, orange juice and vanilla extract to the dry ingredients. Use a hand mixer or whisk to mix the batter until it is smooth and well incorporated, about 2 minutes.
Scoop out 1 cup of the vanilla batter and place it in a separate bowl. Whisk in the cocoa powder until it is fully incorporated and the chocolate batter is smooth.
Alternate spoonfuls of the vanilla and chocolate batters into the prepared baking tin, creating a marble effect. Use a butter knife or skewer to swirl the batters together, creating a marbled pattern.
Bake the marble cake for 35-40 minutes, or until a toothpick inserted into the centre comes out clean.
Allow the cake to cool completely in the tin before slicing and serving.