Preheat oven to 400°F (200°C).
In a mixing bowl, combine chickpeas, olive oil, cumin, coriander, paprika, turmeric, salt, and black pepper. Toss to coat evenly.
Spread the chickpeas on a baking sheet and roast for 20 minutes, stirring halfway through, until crispy.
Warm the pita breads or wraps in the oven for a few minutes.
Assemble the wraps by layering lettuce, tomatoes, cucumber, red onion, and roasted chickpeas. Drizzle with tahini sauce.
Fold the wraps and serve immediately.