The nearly face-on spiral galaxy NGC 3938 has been observed in the H_alpha line with the TAURUS II Fabry-Perot interferometer at the William Herschel Telescope in order to study the kinematics of the ionized gas. We are able to construct intensity, velocity and velocity dispersion maps for this galaxy. The rotation curve of the galaxy is calculated up to 4.5 radial scale lengths from the galactic centre. The residual velocity field shows very small values with no systematic pattern. The mean velocity dispersion is approximately constant with radius at about 11 km s(-1) as previously reported for the neutral and molecular gas. We have also studied the relation between intensity and velocity dispersion for the ionized gas. We have found that this distribution is compatible with a turbulent gas relaxing to a Kolmogorov type turbulence as the stationary regime. The average dispersion varies with intensity as sigma ~ I(1/8) although it becomes much steeper at higher intensities, for which the dispersion is kept almost constant at a value of about 19 km s(-1) . Based on observations made with the William Herschel Telescope operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias