Lightly pack petals into a lidded pint jar. Add vodka (it should just cover petals), then top with lid and chill. Shake after 1 hour, then chill until petals are drained of color, about 2 hours more. Strain vodka into another pint jar and discard petals.
Pour 1/2 cup vodka into first pint jar (save the rest for a future round) and add remaining ingredients. The color will transform from brownish to pink. Drop in several ice cubes and shake until cold, then strain into two cocktail glasses and garnish each with a rose petal.
*Find simple syrup at liquor stores, or make your own: In a glass measuring cup, combine 1/4 cup each sugar and water. Microwave until simmering, then stir until sugar dissolves. Chill syrup until cold.
Make ahead: Rose vodka, up to 4 months, chilled airtight. For brightest cocktail color, use within a week; as the vodka ages, the cocktail will be more peach colored than pink. The rosy flavor remains, though.