In a large mixing bowl, combine the warm water, honey, and instant yeast. Let it sit for 5 minutes until frothy.
Add the gluten free all-purpose flour, salt, and olive oil to the yeast mixture. Stir until a soft, slightly sticky dough forms.
Cover the bowl with a damp towel and let the dough rise in a warm place for 45 minutes.
Divide the dough into 6 equal pieces. On a heavily floured piece of parchment paper, roll each piece into a 6-inch circle about 1/4 inch thick.
Heat a cast-iron skillet over medium-high heat. Carefully transfer a rolled pita onto the hot dry skillet.
Cook for 2 to 3 minutes on the first side until bubbles form, then flip and cook for another 1 to 2 minutes until it puffs up and is lightly browned. Keep warm in a kitchen towel.