Combine sugar, water, and rosemary sprigs in small saucepan. Bring the mixture to a simmer over medium heat, stirring constantly, until the sugar dissolves.

Remove from heat and cover. Let steep for up to 30 minutes. Check after 10 minutes to see if you like the flavor. Let steep longer as desired.

Strain the sprigs out with a fine mesh sieve and let cool completely.

Store in a sealable jar or airtight container in the refrigerator for up to 1 month.