Can buildings be built using Tensegrity, such as skyscrapers?

Yes, but…

If you look at most examples you will notice strictly a framework. A few examples will suspend a bridge or solid form using it or them, as a compression strut.

So you become limited to structures so big the occupied portions look like the struts or a large mass supported by a couple of tendon tied struts.

If you try to cover the thing you get a tensile structure instead.

It could work as a series of platforms, but that may not fit your idea of a building much less a skyscraper.