Starbucks is celebrating National Iced Tea Day – Buy 1 Teavana Shaken Iced Tea and Get 1 FREE (Friday, June 10th, 2016) RMP EditorJune 8, 2016 Starbucks fans – mark your calendars! This Friday, June 10th, Starbucks is celebrating National Iced Tea Day by offering up Buy 1 Teavana Shaken Iced Tea and Get 1 FREE. Visit Starbucks for more info!