Combine the orange juice, water, and granulated sugar in a saucepan, then heat over medium heat for 3 to 5 minutes.
Once the liquid is warm, mix in the fresh or frozen cranberries and a cinnamon stick.
Heat the mixture to boiling, then immediately turn it down to medium heat. Continuously stir the cranberries as they simmer for 10 to 15 mins, or until all the cranberries pop.
Remove the cinnamon stick from the cranberry sauce, then transfer the cranberry sauce to a serving bowl. Allow the sauce to cool in the refrigerator for 30 minutes, then enjoy!