Combine first 4 ingredients in a saucepan. Bring to a boil; cook 3 minutes or until sugar dissolves. Remove from heat; chill. Strain basil mixture through a sieve into a bowl, pressing basil with the back of a spoon to remove as much liquid as possible. Discard basil. Combine sugar mixture and juice.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 1 hour or until firm. Remove sorbet from freezer 10 minutes before serving.