In a saucepan, bring the cranberry juice, clementines, cloves, and cinnamon sticks up to a boil. Remove the pan from the heat and set aside. This will infuse the tangerines and spices into the juice. Chill the infused juice completely.
In a punch bowl, whisk the chilled juice, soda, and rum together. Chill the punch completely before serving. Serve the punch in a pretty punch bowl and ladle into glasses filled with ice.