Preheat oven to 350°.
To prepare cake, pour 2/3 cup boiling water over 6 tea bags in a bowl; steep 10 minutes. Remove and discard tea bags; cool tea to room temperature. Stir in sour cream.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt, stirring with a whisk. Place granulated sugar and butter in a large bowl; beat with a mixer at medium speed until well blended (about 5 minutes). Add eggs, 1 at a time, beating well after each addition. Beat in vanilla. Add flour mixture and brewed tea mixture alternately to sugar mixture, beginning and ending with flour mixture; mix after each addition. Spoon batter into a 10-inch tube pan coated with cooking spray. Bake at 350° for 1 hour and 10 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 15 minutes on a wire rack. Remove from pan; cool completely on wire rack.
To prepare glaze, pour 1/4 cup boiling water over 1 tea bag in a medium bowl; steep 5 minutes. Remove and discard tea bag. Add powdered sugar and juice to brewed tea, stirring well with a whisk. Drizzle glaze over cake.