In a small saucepan, combine the water, sugar, and cinnamon sticks. Bring to a simmer over medium heat, stirring occasionally until the sugar dissolves. Reduce heat and let it simmer for about 10 minutes to allow the cinnamon flavor to infuse.
Remove from heat, let it cool, and strain out the cinnamon sticks. Store the syrup in an airtight container in the fridge for up to 2 weeks.
This recipe yields about ½ cup of cinnamon syrup, which is enough for around 8 cocktails (assuming each drink uses ½ oz of syrup).