Bring water to a boil in a saucepan over high heat. Stir in sugar, cinnamon stick, and star anise. Remove from heat and add tea bags. Let steep for 3 minutes (or according to package directions for strongest tea). Remove tea bags. Let cool to room temperature, about 1 hour. Remove and discard cinnamon stick and star anise.
Stir together tea mixture, orange juice, whiskey, and lemon juice in a punch bowl or pitcher. Chill until cold, about 2 hours or up to overnight.
Garnish with tangerine slices and additional star anise. Ladle into ice-filled glasses. Top each with a tangerine slice.