In a large bowl, combine strawberries and sugar; let stand until juicy, about 1-1/2 hours. Process in batches in a blender until pureed, Add milk, orange juice and cinnamon; cover and process until blended.
Fill cylinder of ice cream freezer two-thirds full; freeze according to manufacturer's directions. Refrigerate remaining mixture until ready to freeze. Transfer sherbet to freezer containers, allowing headspace for expansion. Freeze 2-4 hours or until firm. Repeat with remaining sherbet mixture.