Cook the gluten-free pasta according to package instructions.
Prepare the vegetables: halve the cherry tomatoes, dice the cucumber and bell pepper, and slice the red onion.
In a large bowl, combine the cooked pasta, prepared vegetables, chickpeas, and feta cheese.
In a separate small bowl, whisk together olive oil, lemon juice, dried oregano, salt, and pepper.
Pour the dressing over the pasta salad and toss to combine thoroughly.
Add the chopped parsley last and toss lightly before serving.
Taste and adjust seasoning if needed, then serve chilled or at room temperature.