Combine the rhubarb, sugar, and water in a saucepan and place over medium heat. Bring it to a gentle simmer and keep it there for 20 minutes. Remove it from the heat, stir in the vanilla extract, and steep until completely cooled.
Strain the syrup through a fine-mesh sieve and decant into a storage container.
To serve you can pour some of the syrup into individual glasses (say, 3 tablespoons per glass) before filling with ice, pouring over seltzer/carbonated water, and stirring gently to combine or make a big batch in a pitcher and serve immediately (figure 6 - 8 fluid ounces of seltzer per serving).
- Save the rhubarb that you've strained from the syrup. Put it on ice cream, Greek yogurt, stir into cake badder, muffins, make jam... you get the idea.