  We have investigated the charge-dependent anisotropic flow in high-energy
heavy-ion collisions, using relativistic resistive magneto-hydrodynamics
(RRMHD). We consider the optical Glauber model as an initial model of the
quark-gluon plasma (QGP) and the solution of the Maxwell equations with source
term of the charged particles in two colliding nuclei as initial
electromagnetic fields. The RRMHD simulation is performed with these initial
conditions in Au-Au and Cu-Au collisions at $\sqrt{s_{\mathrm{NN}}} = 200$ GeV.
We have calculated the charge-odd contribution to the directed flow $\Delta
v_1$ and elliptic flow $\Delta v_2$ in both collisions based on electric charge
distributions as a consequence of RRMHD. Our results show that the $\Delta v_1$
and $\Delta v_2$ are approximately proportional to the electrical conductivity
($\sigma$) of the medium. In the $\sigma=0.023~\mathrm{fm}^{-1}$ case, our
result of $\Delta v_1$ is consistent with STAR data in Au-Au collisions.
Furthermore, in Cu-Au collisions, $\Delta v_1$ has a non-zero value at $\eta =
0$. We conclude that the charge-dependent anisotropic flow is a good probe to
extract the electrical conductivity of the QGP medium in high-energy heavy-ion
experiments.
