It did not happen. The Great Sphinx is carved into stone that stood on the plateau naturally, supplemented by stone blocks for the lower parts, many of which are from later repairs during the New Kingdom, Greek era, Roman era, and modern era. Besides, the Nile is actually farther away from the Sphinx now than it was thousands of years ago.

I think you are probably confusing the Sphinx with the story of the Abu Simbel temples which were moved due to the construction of the Aswan Dam and the resulting rise of the Nile. Or maybe even another temple with the same story like the Temple of Dendur at the Met in NYC.