In a small saucepan, combine apple cider, sugar and cinnamon sticks over medium heat.
Bring to boil and then reduce to a simmer. Simmer for 10-15 minutes, stirring occasionally.
Remove from heat and let cool. The syrup will thicken as it cools.
In a cocktail shaker, combine gin, apple cider syrup and ice. Shake and strain into martini glass.