Combine water and sugar in a saucepan and bring to a boil, turn off heat. Add rosemary sprig and submerge in syrup; let sit for 5-10 minutes, then discard rosemary and chill the syrup until ready to make the cocktails.
To Make the Cocktails
Combine gin, rosemary simple syrup and lemon juice in an ice filled cocktail shaker; shake until thoroughly chilled.
Pour over ice in two tall Collins glasses and top off each cocktail with chilled club soda.