In a small saucepan, heat water to boiling. Add sugar, reduce heat to low, and stir until dissolved. Add pepper and cover. Remove from heat and let stand for 20 minutes to infuse the flavor. Strain into a jar. Let cool completely before using.
Combine vodka, lemon juice, and syrup in a cocktail shaker. Add ice. Shake for 15 seconds. Strain into a glass over ice or straight up in a cocktail glass.