We study DC and AC electrophoresis of silica nano and microrods in a thin film of a nematic liquid crystal. These particles induce virtual topological defects and demonstrate nontrivial electrophoresis. We measure several electrophoretic mobility coefficients and compare with those calculated theoretically. We demonstrate a competing effect of elastic and electrostatic torques that arises due to tilting of the rods in the liquid crystal. A simple theory describing this effect allows us to measure the effective polarisability of the rods. Our approach is simple and applicable to a wide variety of asymmetric and polarisable particles.