An optical method for measuring the conductivity of low-conductivity dielectric liquids is proposed. The method is based on measuring the electric field relaxation times in a cell containing low-conductivity liquid dielectrics, with one electrode coated with a non-conductive dielectric film. The electric field relaxation time in the cell is estimated from the magnitude of the electro-optical Kerr effect, which depends on the field strength. The results of electro-optical conductivity measurements are in good agreement with those obtained using the classical method based on the analysis of current-voltage curves. The effectiveness of the method is confirmed by computer modelling of electric field relaxation using the Nernst-Planck-Poisson equations.