How to meassure a high frequency dirty current?
Edit: Adjusted answer to allow measurement of current.

Place a current sampling device in series with the load such as a low value shunt resistor. This will provide a known current to voltage transformation.

A spectrum analyzer is a good choice for this type of application. You will be able to clearly measure the level of the fundamental signal and observe the level of the harmonics. Make certain to pick a spectrum analyzer with a sufficiently low frequency range. 

You may find a sound card spectrum analyzer that has a high enough range to catch the fundamental frequency. Look for sound card FFT (Fast Fourier Transform) software/hardware and check its high frequency limit.

Take care to account for the common mode voltage between the DUT and the measurement instrument.