Cook the rotini pasta according to package instructions until al dente. Drain and rinse under cold water to cool.
In a food processor, combine basil leaves, Parmesan cheese, pine nuts, garlic, and a pinch of salt. Pulse until finely chopped.
With the food processor running, slowly drizzle in the olive oil until the pesto is smooth and well combined. Adjust seasoning with salt and pepper if needed.
In a large bowl, combine the cooled pasta, cherry tomatoes, cucumber, red bell pepper, and red onion.
Add the pesto to the pasta mixture and toss until everything is evenly coated.
Chill the salad in the refrigerator for at least 30 minutes before serving to allow the flavors to meld.