Stir garbanzo beans, grape tomatoes, cucumber, black olives, red onion, olive oil, garlic, balsamic vinegar, lemon juice, basil, salt, and black pepper in a large salad bowl.
Bring a large pot of lightly salted water to a boil; cook the rotini at a boil until tender yet firm to the bite, about 10 minutes; drain. Gently fold pasta into salad and chill 15 to 20 minutes to blend flavors. Mix feta cheese into salad.