In a large saucepan, combine simple syrup, cinnamon, and orange zest. Bring to a boil over medium-high heat; add cranberries. Cook until cranberries just begin to pop and skins begin to split, about 1 minute. Remove from heat and let cool slightly.Advertisement
Strain liquid into a large container. Discard cinnamon and orange zest; add cranberries to liquid, along with rum. If cranberries are not fully submerged in liquid, add equal parts simple syrup and rum until they are completely covered. Let cool completely.
Cover, and transfer to refrigerator until chilled, at least 2 hours and up to 3 weeks.