Black currant tea's naturally sweet, fruity flavor and aroma stand out in this cake but don't overpower it. If you don't want to pour all the glaze over the cake, drizzle some over individual slices.
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.