Puree strawberries and sugar in a blender until smooth. Transfer to a bowl and stir in Aperol and orange zest. Cover and refrigerate until cold, at least 1 hour and up to 2 hours.
Chill a loaf pan in freezer at least 10 minutes. Freeze and churn strawberry mixture in an ice cream maker according to manufacturer's directions, then transfer to pan. Cover with plastic wrap and freeze until hardened, at least 2 hours; sorbet can be frozen up to 2 weeks ahead.