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We present the first application of a magneto-seismology technique using the MHD theory of asymmetric waveguides. By applying the recently developed Amplitude Ratio Method to chromospheric fibrils, we are able to estimate the local Alfven speed, which has previously been nearly impossible to determine given the observational challenges to directly measure the magnetic field. Solar magneto-seismology (SMS) diagnostics is carried out by approximating the boundaries of the chromospheric dark fibrils using Gaussian fitting, then taking the ratio of the measured maximum amplitudes of each boundary oscillation. This amplitude ratio provides a proxy of the internal magnetic field strength of the fibril as a waveguide and is exploited using a numerical inversion scheme. Five fibrils are analysed as a proof of concept. Their internal Alfven speeds are estimated and agree well with previous studies, demonstrating the powerful diagnostic applicability of SMS to asymmetric MHD waveguides.