All the REGA turntables have the ground in the shielded cable already, your problem is within your system, try plugging all the 3 prongs into a cheap power strip, and the AMP directly in wall. Also, any cables you can change to balanced (XLR) would help cut this out. This video might help clarify.
www.youtube.com/watch?v=GS-6jBk9YPM
Matt M
www.youtube.com/watch?v=GS-6jBk9YPM
Matt M