The first measurement at the LHC of charge-dependent directed flow (v_{1}) relative to the spectator plane is presented for Pb-Pb collisions at sqrt[s_{NN}]=5.02 TeV. Results are reported for charged hadrons and D^{0} mesons for the transverse momentum intervals p_{T}>0.2 GeV/c and 3<p_{T}<6 GeV/c in the 5%-40% and 10%-40% centrality classes, respectively. The difference between the positively and negatively charged hadron v_{1} has a positive slope as a function of pseudorapidity η, dΔv_{1}/dη=[1.68±0.49(stat)±0.41(syst)]×10^{-4}. The same measurement for D^{0} and D[over ¯]^{0} mesons yields a positive value dΔv_{1}/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 Δv_{1} of charged hadrons and D^{0} 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 dΔv_{1}/dη for both light flavor and charmed hadrons.