That's a reasonable, practical way to measure the approximate inductance. A couple of things to keep in mind:
(1) You're actually measuring the impedance magnitude, which will include both the resistive and inductive components of the impedance (but the resistive component is probably small compared with the inductive component);
(2) Assuming you're using true-RMS meters to measure both the current and the voltage, your estimate of the impedance will be affected by the harmonic voltages coming out of your variac, which in turn will come both from any distortion in your AC source as well as from any non-linearities in the variac (but these are both probably small, so they shouldn't affect the measurement much).
You can compensate for (1) by measuring the resistance of the inductor, and removing that component from your measurement. The resistance is probably too low to measure easily with an ohm-meter; instead, with the inductor disconnected from AC, take a constant-current bench-top DC supply and force a couple of amps of DC current through the inductor, and measure the DC current and the DC voltage drop across the inductor - that will tell you the inductor's resistance to within a few milliohms.
If you want to know the precise inductive impedance, you can either use a pure sinusoidal voltage (difficult), or you can put the unknown inductor in parallel (or series) with a known-value precision capacitor and measure the frequency of the resonant peak.