Cook the tortellini according to the package directions, reserving 1/4 cup of the cooking liquid.
Meanwhile, heat the oil in a large skillet over medium heat. Add the onion and cook until softened, about 5 minutes. Add the sausage and cook, crumbling it until browned, about 7 minutes. Add the garlic, spinach, salt, and pepper and cook, tossing frequently, until the spinach wilts, about 3 minutes.
Add the drained tortellini, the reserved cooking liquid, and the parmesan and toss.