In a 6-quart Dutch oven or kettle, stir together cider, lemon juice, and sugar. Add cinnamon sticks. Insert a whole clove in the peel side of each orange wedge. Add to cider mixture.
Bring to boiling; reduce heat. Cover and simmer for 30 minutes. Remove orange wedges and cinnamon sticks with slotted spoon, if you like. Makes 16 to 18 (8-ounce) servings.