I don't think they say "ten rings" out loud, but they have a banner with this logo:



Raza, the leader of the Afghan terrorist gang in the first film, wears a bulky ring on his the ring finger of his left hand, and refers at some point to "the man whose ring I wear". When Obediah Stane paralyzes Raza, he takes the ring.

Justin Hammer, the competitor who gets Whiplash freed from prison in the second movie, also wears a bulky ring on his left pinky.