Bring a large pot of salted water to a boil.
Add the gluten-free pasta and cook according to package directions, about 8 to 10 minutes.
Drain and rinse the pasta under cold running water until cooled.
Toast the pine nuts in a small skillet over medium heat for 3 to 5 minutes, stirring often, until golden and fragrant.
Add the toasted pine nuts and garlic to a food processor and blend until finely broken down.
Add the basil leaves and lemon juice, then blend until finely chopped.
Add the olive oil, salt, and black pepper, then blend until incorporated.
Toss the cooled pasta with the pesto, cannellini beans, and cherry tomatoes.
Store in an airtight container in the refrigerator until ready to serve.
Stir in the arugula just before serving.