The first measurement at the LHC of charge-dependent directed flow (v1) relative to the spectator plane is presented for Pb-Pb collisions at sNN=5.02 TeV. Results are reported for charged hadrons and D0 mesons for the transverse momentum intervals pT>0.2 GeV/c and 3<pT<6 GeV/c in the 5%-40% and 10%-40% centrality classes, respectively. The difference between the positively and negatively charged hadron v1 has a positive slope as a function of pseudorapidity η, dΔv1/dη=[1.68±0.49(stat)±0.41(syst)]×10-4. The same measurement for D0 and D¯0 mesons yields a positive value dΔv1/dη=[4.9±1.7(stat)±0.6(syst)]×10-1, which is about 3 orders of magnitude larger than the one of the charged hadrons. These measurements can provide new insights into the effects of the strong electromagnetic field and the initial tilt of matter created in noncentral heavy ion collisions on the dynamics of light (u, d, and s) and heavy (c) quarks. The large difference between the observed Δv1 of charged hadrons and D0 mesons may reflect different sensitivity of the charm and light quarks to the early time dynamics of a heavy ion collision. These observations challenge some recent theoretical calculations, which predicted a negative and an order of magnitude smaller value of dΔv1/dη for both light flavor and charmed hadrons.