Stir all ingredients except reserved 1/3 cup cranberries in a small saucepan until combined.
Cook over LOW heat, stirring occasionally, until cranberries start to soften (about 10 minutes).
Increase heat to MEDIUM/LOW. Continue to cook, stirring occasionally until the cranberries burst (about 5 minutes).
Stir in remaining cranberries. Cook for 1 to 2 minutes until the added cranberries start to soften. Taste and adjust for seasoning--add more sugar or orange juice, if necessary.
Remove cinnamon stick and allow cranberry sauce to cool before serving.