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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. We test the hypothesis vγ,dir2≡0 for 0.9<pT<2.1 GeV/c and obtain a significance of 1.4σ for the 0-20% class and 1.0σ for the 20-40% class. A comparison to RHIC data shows a similar magnitude of the measured elliptic flow, while hydrodynamic and transport model calculations predict a smaller flow than observed.