Soak red onion in a bowl of ice water in refrigerator to remove strong taste, at least 30 minutes. Drain and rinse.
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 8 minutes; drain and rinse under cold water.
Mix onion, pasta, tuna, celery, roasted red peppers, sun-dried tomatoes, feta cheese, parsley, basil, capers, and Greek dressing together in a large bowl. Allow to marinate in refrigerator, 4 hours to overnight.