Purée berries in a food processor, then rub through a fine strainer into a medium bowl. Discard solids. Stir in remaining ingredients.
Freeze mixture in an ice cream maker according to manufacturer's directions.
Transfer to an airtight container and freeze until firm enough to scoop, at least 4 hours and up to 2 weeks.
Note: Nutritional analysis is per 1/2-cup serving.