Combine 1/4 cup sugar and 1/2 cup salt on a small plate. Run a wedge of grapefruit around the rim of 4 glasses to moisten the rims. Lightly dip the rims in the sugar mixture and set aside to dry.
Combine the grapefruit juice, tequila, lime juice, sugar syrup, and a pinch of salt together in a pitcher. Fill a cocktail shaker 1/2 full with ice and pour in the drink mixture. Shake the cocktail shaker for 30 seconds to chill and dilute the drink. Pour into the 4 prepared glasses, add a few ice cubes, and a wedge of grapefruit and serve ice cold.
To make sugar syrup, combine 1 cup sugar and 1 cup water in a small saucepan and bring to a boil over medium heat. Cook until the mixture is clear. Cool and refrigerate indefinitely.