How can a crew be warned of "Clear Air Turbulence" during the flight?
Not on board the aircraft as of yet, no (unless, as @Gerry said, you count the radio that lets you hear about the person ahead of you running into CAT).

There are ways of detecting CAT, however, which could become standard aircraft equipment in the future.  LIDAR is one possibility, as both @Gerry and @mins mentioned; see also here and here.  Interestingly, the idea of using LIDAR to detect clear-air turbulence has been around since at least the late 60s, but, when it was first proposed, they couldn't get the sensitivity high enough; later, when this obstacle was overcome, they faced a different problem, which was that the equipment required was far too heavy, bulky, and power-hungry to be practical, which remained the case until very recently.  N-slit interferometry can also be used to detect clear-air turbulence (see here, for instance), and an interferometric (I think; the patent description is remarkable in its unintelligibility) CAT detector was patented in 1978, but the equipment required is far too large to fit on an aircraft; as a result, most work with interferometric CAT detection seems to have been in the area of developing a ground-based clear-air turbulence detector that could monitor runway approaches for dangerous CAT.