Mix water, sugar, and rosemary together in a small saucepan.

Stirring occasionally will help the sugar dissolve while you bring the mixture to a boil.

Simmer for 5 to 10 minutes, or until the syrup has slightly thickened, on low heat.

Turn off the heat and let the syrup to cool in the pan.

To get rid of the rosemary sprigs, filter the syrup through a fine-mesh strainer.

When you're ready to use it, pour the syrup into a clean container and place it in the refrigerator.