Preheat the oven to 400 degrees F.
Put the oil and onions in a medium skillet and cook over very low heat, stirring occasionally, until onions are soft and caramelized, about 15 minutes. Turn the heat up to medium and add the arugula. Cook until the arugula is wilted, about 1 minute. Season with salt and pepper.
Place the tortillas on a baking sheet and top each with some of the arugula/onion mixture. Crumble some goat cheese on top of each, and bake for 10 minutes. Allow to cool for a few minutes and cut each pizza into 4 triangles.