Muon Spin Relaxation and Avoided Level Crossing (ALC) measurements of ferrocene are reported. The main features observed are five high field resonances in the ALC spectrum at about 3.26, 2.44, 2.04, 1.19 and 1.17 T, for the low-temperature phase at 18 K. The high-temperature phase at 295 K shows that only the last feature shifted down to about 0.49 T and a muon spin relaxation peak at about 0.106 T which approaches zero field when reaching the phase transition temperature of 164 K. A model involving three muoniated radicals, two with muonium addition to the cyclopentadienyl ring and the other to the metal atom, is postulated to rationalise these observations. A theoretical treatment involving spin-orbit coupling is found to be required to understand the Fe-Mu adduct, where an interesting interplay between the ferrocene ring dynamics and the spin-orbit coupling of the unpaired electron is shown to be important. The limiting temperature above which the full effect of spin-orbit interaction is observable in the muSR spectra of ferrocene was estimated to be 584 K. Correlation time for the ring rotation dynamics of the Fe-Mu radical at this temperature is 3.2 ps. Estimated electron g values and the changes in zero-field splittings for this temperature range are also reported.