Grate 4 teaspoons orange peel from oranges; place in a bowl.
Using a sharp knife, cut remaining peel and all white membrane from oranges; coarsely chop oranges and place in a colander to drain.
Whirl cranberries in a food processor or blender until chopped; place in bowl with peel.
Add drained chopped oranges, onion, oil, cilantro, ginger, and chile.
Stir to blend; season to taste with salt.