The polarization of photons produced in radiative ${B}_{s}^{0}$ decays is studied for the first time. The data are recorded by the LHCb experiment in $pp$ collisions corresponding to an integrated luminosity of $3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at center-of-mass energies of 7 and 8 TeV. A time-dependent analysis of the ${B}_{s}^{0}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\gamma}$ decay rate is conducted to determine the parameter ${\mathcal{A}}^{\mathrm{\ensuremath{\Delta}}}$, which is related to the ratio of right- over left-handed photon polarization amplitudes in $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ transitions. A value of ${\mathcal{A}}^{\mathrm{\ensuremath{\Delta}}}=\ensuremath{-}0.9{{8}_{\ensuremath{-}0.52}^{+0.46}}_{\ensuremath{-}0.20}^{+0.23}$ is measured. This result is consistent with the standard model prediction within 2 standard deviations.