Preheat the oven 400 degrees F. and line a baking sheet with parchment paper.
In a small bowl, pour the drained chickpeas and dry them with a paper towel.
Add the olive oil, chili powder, smoked paprika, cayenne pepper, salt, pepper, and stir until the chickpeas are well coated.
Pour the chickpeas onto the prepared baking sheet and spread them out into an even layer.
Place into the oven and allow them to bake for 15 to 20 minutes; until golden and crispy on the outside.
In a small bowl, make the tzatziki sauce by stirring together the yogurt, cucumber, lemon vinegar, garlic powder, and dill until combined.
Assemble the gyro by spreading some tzatziki onto one side of the pita.
Divide ¼ of the spicy chickpeas onto each pita followed by the onion, lettuce, and tomato.
Fold in half and serve.