A time-dependent analysis of the B0s→ϕγ decay rate is performed to determine the CP -violating observables Sϕγ and Cϕγ and the mixing-induced observable AΔϕγ. The measurement is based on a sample of pp collision data recorded with the LHCb detector, corresponding to an integrated luminosity of 3  fb−1 at center-of-mass energies of 7 and 8 TeV. The measured values are Sϕγ=0.43±0.30±0.11, Cϕγ=0.11±0.29±0.11, and AΔϕγ=−0.67+0.37−0.41±0.17, where the first uncertainty is statistical and the second systematic. This is the first measurement of the observables S and C in radiative B0s decays. The results are consistent with the standard model predictions.