This is the standard method, but there are a few wrinkles.If you place a resistance in series with the current, then you get a voltage waveform that is dependent on the current (E = IR).
What do you mean 'non-inductive'? There will always be parasitic inductance, albeit, it can be low: ~nH. Believe it or not, using a 0.1Ω current sense resistor with a current shunt monitor will have nH worth of inductance and will kill accuracy when the signal is a sine wave.This is the standard method, but there are a few wrinkles.
You need a low value resistor, so as not to disturb the circuit too much. Look to make the ohms law voltage a few hundred millivolts. Make sure the resistor has enough power capacity for the expected current.
If your ac signal has a frequency greater than a few hundred hertz then you must use a non inductive resistor. Since low value resistors are often wire wound it is worth checking the type. Non inductive wire wounds are made by winding either in a zig zag or by doubling the wiring and winding on a former.
I think we are talking powerline frequencies here or at highest a few hundred hertz.parasitic inductance