We present measurements of π(-) and π(+) elliptic flow, v(2), at midrapidity in Au+Au collisions at √[s(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 π(-) (π(+)) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at √[s(NN)]=27 GeV and higher. At √[s(NN)]=200 GeV, the slope of the difference of v(2) between π(-) and π(+) 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.