The charge transport in thin thermal silicon oxide films treated in electron cyclotron resonance hydrogen plasma at different exposure times was investigated. X-ray photoelectron studies show that such treatment leads to the oxygen deficiency of the films. It was established that the treatment of the films in plasma leads to an increase of their conductivity by a factor of about 102. The film charge transport properties were studied at different temperatures and analyzed within four theoretical dielectric conductivity models. It was found that the charge transport mechanism is described by Fowler-Nordheim model in the initial silicon oxide and by the model of phonon-assisted electron tunneling between neutral traps after the treatment in hydrogen plasma. The thermal trap ionization energy value (Wt = 1.6 eV) measured from transport experiments is in agreement with that obtained from ab initio calculations for the oxygen vacancy (Si-Si bond) in SiO2.