We present here a new free space method to measure the magnetic permeability of a single amorphous magnetic microwire (AMM) at microwave frequencies. The technique consists in inducing a high frequency electric current along the AMM axis by illumination with an electromagnetic wave at antenna resonance conditions. Fitting the induced electric current to the Hallen-Pocklington equation allows computing the relative magnetic permeability of the microwire as a function of the wave frequency. The method results particularly useful for the study of the giant magnetoimpedance effect of AMM by measuring the magnetic permeability upon the application of DC magnetic fields.