As mentioned in the comments, you can use a simple syrup to replace the sugar. A simple syrup is made by either 1:1 ratio of 1:2 ratio of water to granulated sugar (depending how thick you want the syrup to be). Heat until just starting to boil and sugar is dissolved.
I personally like just using the granulated sugar because I feel like it dissolves just fine in the juice but if you are wanting to make sure that it is perfectly smooth, a simple syrup is a great solution. I would recommend cooling the syrup before using it though, or adding a lot of ice because I like this drink coldy cold cold! :D