Place the sugar water and cinnamon stick in a small saucepan over medium high heat. Bring to a boil, reduce heat and simmer for 5-8 minutes, depending on how strong you want the cinnamon flavor to be. Remove from heat and cool completely. May be stored for up to 1 month in a glass jar in the refrigerator.

Make the cocktail. Place the apple juice, rum and cinnamon infused simple syrup in a cocktail shaker filled halfway with ice. Shake vigorously for 10 seconds. Strain drink into a martini glass. Serve immediately, garnished with a cinnamon stick or apple slice, if desired.