In a saucepan, combine sugar, water and basil. Simmer until sugar is dissolved, about 10 minutes. Strain the syrup, and chill in refrigerator for an hour.
Mix in orange juice, and strain the mixture.
If using ice cream maker, process mixture in it according to manufacturer’s instructions. Transfer to an airtight container, cover and freeze until firm, at least 4 hours.
If not using ice cream maker, pour mixture into a shallow non-stick banking pan. Freeze until frozen, about 2 hours.
Leave the mixture in room temperature for 15 minutes to soften from the edges. Use a fork to scrape big chunks of mixture into a food processor or blender to blend until smooth. If it starts to melt, put it back in the freezer for 5 minutes.
Immediately scoop the sorbet and serve.