In 1-quart saucepan, mix 1/2 cup of the orange juice, the sugar and orange peel. Heat to boiling over medium-high heat, stirring until sugar dissolves. Remove from heat; cool 5 minutes. Refrigerate 30 minutes or until chilled.
In food processor, place strawberries and lime juice. Cover; process until smooth. Gradually add chilled sugar syrup, vodka and remaining 2 1/2 cups orange juice, Cover; process just until blended. Pour into ice-cream freezer; freeze according to manufacturer’s directions.