Preheat oven to 400° F. Lightly grease a muffin tin with cooking spray or vegetable oil, or line with paper muffin liners.
In a medium bowl, whisk together oats, flour, baking powder, baking soda, and salt.
In a large bowl, whisk sour cream, orange rind, orange juice, sugar, oil, and egg until mixture is smooth.
Add flour mixture and stir until ingredients are just combined.
Gently fold in blueberries and cranberries.
Spoon batter into prepared muffin tins and bake for 10 – 15 minutes, or until a toothpick inserted into the center of the muffin comes out clean.