Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1 cup cooking water, then drain.
Meanwhile, heat 1/4 cup olive oil in a separate large pot over medium-high heat. Add the corn and cook, stirring, until browned, 4 to 6 minutes. Add the tomatoes and cook until bursting, 2 to 3 minutes; season with salt and pepper.
Add the pasta, 1/2 cup reserved cooking water and the remaining 2 tablespoons olive oil to the pot with the tomatoes. Cook, stirring, until coated, adding more cooking water if needed; season with salt and pepper.
Remove from the heat and stir in the goat cheese. Working in two batches, add the arugula and stir until lightly wilted.