According to Wikipedia:
‘Tutting’ refers to a distinct style gained usage during the early 1980s. Its movements made use of the wrists, elbows, and shoulders to create the desired right angle.
Presumably, the dance began as a mimicking of the angular poses common to ancient Egyptian art. Tutting as a whole or certain tutting moves have been referred to as ‘King Tut'; it is likely from this colloquialism for the Pharaoh Tutankhamen, as a representative of ancient Egypt in western popular culture, that the form gained its name.