1. Devein shrimp, if desired.
2. Whisk together olive oil and next 6 ingredients in a large bowl. Pour mixture into a large zip-top plastic freezer bag; add shrimp, turning to coat. Seal and chill 3 to 8 hours, turning occasionally. Drain shrimp mixture, and stir in oranges and basil. Spoon mixture into chilled glasses or small serving bowls.