In a medium mixing bowl, whisk together ice water, tempura batter mix, and cayenne pepper just until large lumps disappear. Batter will be lumpy; set aside.
In a small bowl, combine sour cream, ranch dressing, and hot sauce; set aside.
Heat oil in saucepan to 375 degrees F.
Pat dry olives with paper towels. Dip olives into tempura batter, slightly shake off excess, and carefully slide into oil. Do not crowd the pan. Fry for 3 to 5 minutes, until golden. Remove with slotted spoon and drain on paper towels. Skim batter pieces from oil between batches.
Serve with dipping sauce.