Make the rosemary syrup ahead: combine the sugar, water and 3 rosemary sprigs in a small saucepan, bring to a simmer over medium heat for 3 minutes until the sugar dissolves and the syrup coats the back of a spoon, then cool and strain.
Fill a wine glass with ice cubes to the rim.
Pour in the cranberry juice and 0.75 oz of the cooled rosemary syrup.
Top with the chilled club soda and give the glass one gentle stir with a long spoon so the bubbles stay intact.
Thread the fresh cranberries onto a cocktail pick and rest it across the rim alongside the extra rosemary sprig.
Serve immediately while the spritz is still fizzing.
Good to Know
The rosemary syrup keeps in a sealed jar in the fridge for two weeks, enough for six spritzes without repeating the stovetop step.