Rinse the chickpeas under cold water and let them drain well.
In a large mixing bowl, combine chickpeas, cherry tomatoes, cucumber, red onion, feta cheese, and parsley.
In a separate bowl, whisk together olive oil, red wine vinegar, oregano, salt, and pepper. Pour over the chickpea mixture and toss gently.
Lay out tortillas and place a handful of spinach or mixed greens in the center of each.
Spoon the chickpea mixture evenly onto the greens.
Fold in the sides of the tortilla and roll tightly from the bottom to the top.
Heat a non-stick skillet over medium heat and cook wraps seam-side down for 2-3 minutes on each side until golden brown and crispy.
Let cool for a minute before slicing in half and serve immediately.