In a cocktail shaker, combine the vodka, juice, and syrup with ice. Shake for about 15 seconds, then pour through a strainer into the martini glass. Garnish with a fresh sprig of rosemary.
For rosemary simple syrup
Combine 1 c water and 2-3 sprigs of fresh rosemary in a pan. Bring the water to a boil, then reduce the heat to a simmer. Simmer for 5 minutes.
Add 1 c sugar to the simmering brew. Stir until the sugar is fully dissolved into the water. Pour into a jar, making sure to pick or strain out the sprigs of rosemary as you pour.