If I am reading you right then it doesn't hum unless you touch the plug?

It's a ground loop, not uncommon if you are using a turntable but can happen with other equipment too.

Can be very hard to track down the cause. It doesn't necessarily mean that anything is faulty.

Do you use a grounding wire from turntable to amplifier? Most TTs have one and most amps with phono stages with have a connecter to hook it up to. If you are try disconnecting it, if not then try connecting it, see if the problem persists.

If it really only happens when you touch the plug then I would just avoid touching the plug, and not worry about it.