In this paper we present a novel apparatus aimed at measuring very small birefringences and anisotropies, based on frequency metrology and not on polarimetry as usual. In our experiment, a very high finesse resonant cavity is used to convert the phase difference into a resonance frequency difference, which can then be measured with very high accuracy. We describe the set-up and present the results of experimental tests which exhibited a sensitivity dn ~ 2 x 10−18, allowing for the measurement of long-predicted magneto-electro-optical effects in gases. Since the shotnoise limited sensitivity of our apparatus lies well below the state-of-the-art sensitivity, frequency metrology appears as a promising technique for small birefringence measurements.