Preheat oven to 350°F and line baking sheets with parchment paper.
In a medium bowl, whisk together the gluten-free flour, cocoa powder, baking soda, and salt.
In a large bowl, cream the butter and sugar until light and fluffy, then beat in the egg and vanilla extract.
Gradually mix the dry ingredients into the wet ingredients until well combined.
Roll dough into 1-inch balls and place 2 inches apart on prepared baking sheets.
Bake for 10-12 minutes until edges are set.
Immediately sprinkle crushed candy canes over the hot cookies and gently press to adhere.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.