Put the annatto seeds, oregano, cumin seeds, peppercorns, and cloves in a small food processor or spice grinder. Grind until all of the spices are broken down into a fine powder.
Squeeze the juice of half the orange and the lime into a small bowl. Remove any seeds from the bowl.
Add the orange juice, lime juice, garlic cloves, salt, coriander, and white vinegar to the food processor. Add the ground seeds as well. Blend until a thick paste forms. The achiote paste is ready to serve.