Cook the pasta according to package directions. Reserve 1/2 cup of the pasta water, drain, and return the pasta to the pot.
Meanwhile, heat the oil in a large skillet over medium heat. Add the zucchini and 1/2 teaspoon salt. Cook, tossing often, until just tender, 4 to 5 minutes. Add the chickpeas, garlic, and red pepper and cook until heated through, 2 to 3 minutes.
Toss the pasta with the reserved pasta water. Divide the pasta among bowls and top with the zucchini mixture.