A new and distinct cultivar of Azalea plant named `Pink Angora`, characterized by its dark green-colored leaves that do not abscise during the cooling and forcing periods; uniform and outwardly spreading plant habit; freely branching habit; uniform and freely flowering habit; rapid flowering response; plants begin flowering about three weeks after cooling treatment; large and showy bright pink-colored flowers; double hose-in-hose flower form; flowers star-shaped; good postproduction longevity with plants maintaining good flower substance for about three to four weeks in an interior environment; and very good resistance to Cylindrocladium in inoculated trials.