Measure current in high voltage (10kV)

You could use a transformer to multiply up the current.

The image shows a current transformer working in the normal way for measuring very high currents. The measured current will be 1/N times that in the red cable. Basically you want to do the opposite.

Get a large iron ring, and loop your cable through it 10x. Then loop another small wire through the ring and measure the current in that.

12 mVpp is a decent signal, and well above noise floor of reasonable electronics. Using a current transformer as you are doing is a good idea since it inherently isolates the current signal from the high voltage. As long as that signal has good signal to noise ratio, you are fine. 12 mVpp is high enough that it should not be hard to amplify it as neeed without adding significant noise. Since this is AC, you don't have to worry about DC offsets.

This is really not a hard problem. You want to detect the amplitude of a AC signal. Consider that AM radios routinely amplitude demodulate much weaker signals. It would help to know the frequency range of both the AC signal (the carrier in AM terms) and what you need the answer to be (the demodulated signal). Without knowing those, it is difficult to make any concrete suggestions.