Cook the rhubarb and sugar in a medium saucepan over medium heat, stirring occasionally. When the rhubarb starts to soften, but before it falls apart—about 5 minutes—use a slotted spoon to transfer it to a bowl. (Save the poached rhubarb to top ice cream or fill shortcakes.)
Cook down the remaining rhubarb liquid in the pan until it thickens and turns syrupy, about 5 minutes longer. You should have about 4 oz./½ cup) of syrup. Cool the syrup over an ice bath. It will thicken further as it cools.
To rim the glasses: Gently run the lemon wedge around the rims of 4 cocktail glasses, removing any clinging pulp. Mix the sugar and ground cinnamon on a small plate. Rim the glasses by turning each moistened rim upside down onto the cinnamon sugar plate. Turn the glasses right side up, fill with ice cubes and set aside while you mix the cocktails.
To make the cocktails: Fill a cocktail beaker (or Mason jar) with 4 oz. rhubarb syrup and 8 oz. vodka, then add ice. (You may have to mix in two batches, depending on the size of your shaker.) Shake for 30 seconds and then strain equal amounts into each of the four glasses. Top with sparkling water and stir gently.