To construct gluten-free Creamsicle Orange Cookies you'll have to use cake mix that is precisely formulated without gluten. Many brands, in stores offer gluten-free choices for cake mix. It's important to make sure that all the other elements you use, like chocolate chips and powdered sugar are also free of gluten. By making these subs you can savor the taste of Creamsicle Orange Cookies while staying mindful of your gluten-free diet.