Determining the ionic mobility in solids is often challenging due to inherently low ionic conductivities, typically requiring measurements at elevated temperatures, with high impedance analyzers and/or extended resistivity transients. Moreover, in many solids, the ionic conductivity is masked by dominant electronic conductivity, characterized by much higher carrier mobility. By focusing our measurements on nano-dimensioned thin films, we are able to overcome such limitations. First, measurement time and temperature can be reduced, the latter to near ambient conditions, in selected materials, due to the considerably faster response of thin films compared to bulk materials to applied electrical stimulus. Second, the effect of the redistribution of ionic defects on the nano-scale, at relatively short time, has a major impact on the total conductivity. The proposed method relies on measuring the nonlinear I-V response of thin films to linear voltage sweeps of high amplitude (relative to the thermal voltage) at different sweep rates. This differs from the impedance spectroscopy technique that analyzes the small signal response of systems. The method also differs from the well-known technique of cyclic voltammetry for deriving ion diffusion coefficients, as it does not require redox reactions to take place during voltage sweeps, thereby making it more generally applicable. In this work, we present a novel and simple method for determining the ionic mobility from the measured I-V relations. It is determined from the position of a peak in the I-V relations and the sweep rate. The mobility so derived is compared with the one obtained by fitting the I-V relations based on solving the drift-diffusion equations for ions and electrons as published recently. Though the near ambient temperature ionic mobility was found to be seven orders of magnitude lower than the corresponding electronic one, it could nevertheless be well deconvoluted and characterized by both methods. The experimental results are compared with previous measurements on bulk and powder samples of molybdenum trioxide.