Use a peeler to remove the zest from the orange in wide strips, leaving the bitter white pith behind. Cut the orange in half and squeeze the juice into a small bowl.
In a saucepan, add sugar, water, cranberries, orange zest, cinnamon stick, and orange juice; stir to combine. Over medium heat, bring to a simmer; then turn the heat to low. Continue cooking at a low simmer, stirring occasionally, until the cranberries have split and the sauce thickens, 15–25 minutes.
Remove the cinnamon stick and orange zest and discard (optional). Transfer the cranberry sauce to a serving bowl. Serve warm or at room temperature. (Note: If making ahead of time, let the cranberry sauce cool before transferring it to an airtight container. Refrigerate for up to 3 days, then serve cold.)