Bring water to a boil. Add sugar and stir until sugar has dissolved.
Add fresh rosemary to the syrup. Remove from heat, set aside and allow the mixture to cool to room temperature.
Once it’s cooled, remove the rosemary from the syrup with a fork.
Discard the rosemary. Pour the syrup into an airtight container and refrigerate.
When kept in the refrigerator, the syrup will keep for 2 weeks.