We present the first measurement of charge-dependent directed flow in Cu + Au collisions at root S-NN = 200 GeV. The results are presented as a function of the particle transverse momentum and pseudorapidity for different centralities. A finite difference between the directed flow of positive and negative charged particles is observed that qualitatively agrees with the expectations from the effects of the initial strong electric field between two colliding ions with different nuclear charges. The measured difference in directed flow is much smaller than that obtained from the parton-hadron-string-dynamics model, which suggests that most of the electric charges, i.e., quarks and antiquarks, have not yet been created during the lifetime of the strong electric field, which is of the order of, or less than, 1 fm/c.