Preheat the oven to 250 degrees F. Line 2 baking sheets with parchment paper.
Combine the sugar and cinnamon in a small bowl. Put the apple peels in a separate bowl and add a few drops of water (this will help the cinnamon sugar stick). Add the cinnamon sugar to the peels and toss to coat. Transfer the peels to the prepared baking sheets, making sure they are in a single layer.
Bake until crisp, about 1 hour. Let cool before using a thin spatula to slide them off the parchment.