Drain apricots in a sieve over a bowl, reserving 1/2 cup syrup. Purée apricots and reserved syrup in a food processor.
Combine purée, nectar, and remaining ingredients, stirring until sugar dissolves
Pour mixture into 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.