  We present measurements of $\pi^-$ and $\pi^+$ elliptic flow, $v_2$, at
midrapidity in Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200, 62.4, 39, 27,
19.6, 11.5 and 7.7 GeV, as a function of event-by-event charge asymmetry,
$A_{ch}$, based on data from the STAR experiment at RHIC. We find that $\pi^-$
($\pi^+$) elliptic flow linearly increases (decreases) with charge asymmetry
for most centrality bins at $\sqrt{s_{_{\rm NN}}} = \text{27 GeV}$ and higher.
At $\sqrt{s_{_{\rm NN}}} = \text{200 GeV}$, the slope of the difference of
$v_2$ between $\pi^-$ and $\pi^+$ as a function of $A_{ch}$ exhibits a
centrality dependence, which is qualitatively similar to calculations that
incorporate a chiral magnetic wave effect. Similar centrality dependence is
also observed at lower energies.
