The azimuthal anisotropy coefficient v2 of prompt D0, D+, D∗+, and Ds+ mesons was measured in midcentral (30%-50% centrality class) Pb-Pb collisions at a center-of-mass energy per nucleon pair sNN=5.02 TeV, with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays at midrapidity, |y|<0.8, in the transverse momentum interval 1<pT<24 GeV/c. The measured D-meson v2 has similar values as that of charged pions. The Ds+ v2, measured for the first time, is found to be compatible with that of nonstrange D mesons. The measurements are compared with theoretical calculations of charm-quark transport in a hydrodynamically expanding medium and have the potential to constrain medium parameters.