In a small or medium saucepan, whisk together water and sugar. Add ginger slices and bring to a simmer. Simmer for 5 minutes, then turn off the heat and let sit for 10 minutes to allow the flavor to continue to infuse.
Place a strainer over a jar and strain out the ginger from the syrup. Let cool before using. Store in the fridge in an airtight container for up to 2 weeks.
This recipe makes approximately 1 1/2 cups of simple syrup. Halve it to make about 3/4 cups.