The elliptic flow of inclusive and direct photons was measured at mid-rapidity in two centrality classes 0–20% and 20–40% in Pb–Pb collisions at sNN=2.76 TeV by ALICE. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the detector material with the e+e− pairs reconstructed in the central tracking system. The results of the two methods were combined and the direct-photon elliptic flow was extracted in the transverse momentum range 0.9 < pT < 6.2 GeV/c. A comparison to RHIC data shows a similar magnitude of the measured direct photon elliptic flow. Hydrodynamic and transport model calculations are systematically lower than the data, but are found to be compatible.