Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain.
Meanwhile, heat the olive oil in a Dutch oven or large pot over medium-high heat. Add the bell pepper and cook, stirring occasionally, until just tender, about 3 minutes. Add the chickpeas, garlic, red pepper flakes and 1/2 teaspoon salt and cook, stirring occasionally, until the garlic is lightly browned, about 3 minutes.
Add the olives, pasta and the reserved pasta cooking water to the pot; cook 1 minute. Remove from the heat and stir in the arugula and oregano until wilted. Season with salt and pepper. Top with the feta and drizzle with olive oil.