Using (10087±44)×106J/ψ events collected with the BESIII detector, we search for the rare decay J/ψ→γD0+c.c. for the first time. No obvious signal is observed and the upper limit on the branching fraction is determined to be B(J/ψ→γD0+c.c.)<9.1×10−8 at 90\% confidence level.