Yes, a titanium Rolex does exists, albeit only a prototype
I am the proud father of a son who is a qualified Ocean Yacht Master. Emotionally (if not academically) my wife and I went through every stage with him from the obscurity of celestial navigation to his final exam where he captained a fully crewed yacht from Cowes to the Azores and back again. The experience left me with huge appreciation of sailing, and I am an avid follower of the America’s Cup. The craft and crews are simply phenomenal, at the peak of their ability.
In the 2021 race Ben Ainslie, captain of Team Ineos, was spotted wearing a striking watch which has spawned many features online. It was a one-off Rolex Yacht-Master 42, made from Anthracite Titanium. It will never be commercially available and there are very few close-up images of it.
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Sir Ben Ainslie wearing the Rolex Yacht-Master 42 prototype during the America's Cup - Image credit The Times.
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The Rolex Explorer II in Oystersteel (no titanium, sadly) - Image credit WatchGecko.