With modern data acquisition technology, Electrical Resistivity Tomography (ERT) surveys can be deployed easily and run cost-efficiently over large areas and over long periods. Inversion of the electric potential data to image the subsurface resistivity distribution is a key step in the workflow. In contrast to deterministic inversion commonly used in ERT, geostatistical inversion methods construct a variety of possible realizations of resistivity distributions and allow for a better interpretation of results and a quantification of the uncertainty. In this paper we present a geostatistical approach for the inversion of ERT survey data based on Random Mixing. The method of Random Mixing had been developed and tested for inverse groundwater modelling and is applied here to ERT as an example of geophysical inversion for the first time. Random Mixing is based on the idea of constructing realizations of the unknown electric conductivity field by combining random fields representing the spatial correlation of conductivity such that direct measurements of conductivity if available and indirect dipole measurement of electric potentials at electrodes are matched. Implementation is based on the three-dimensional finite element method to solve the forward model where properties in a core region are updated through the Random Mixing iteration. To reduce computational costs for the evaluation of the misfit cost function one-dimensional interpolation is applied. The results of Random Mixing for a synthetic example and a field survey inversion are discussed and compared with deterministic inversion results.