Rub the lemon wedge on the outside rim of the chilled glass. Holding the glass at a 45-degree angle, dip the outside rim in the sugar, rotating as you do, so the entire rim is coated with sugar. (Avoid getting any sugar inside the glass.)
Place the vodka, lemon juice, and simple syrup in a cocktail shaker and fill halfway with ice. Shake vigorously until the outside of the shaker is frosted. Strain into the sugar-rimmed glass and garnish with the lemon twist.