Using (10 087±44)×10^{6} J/ψ events collected with the BESIII detector, the radiative hyperon decay Σ^{+}→pγ is studied at an electron-positron collider experiment for the first time. The absolute branching fraction is measured to be (0.996±0.021_{stat}±0.018_{syst})×10^{-3}, which is lower than its world average value by 4.2 standard deviations. Its decay asymmetry parameter is determined to be -0.652±0.056_{stat}±0.020_{syst}. The branching fraction and decay asymmetry parameter are the most precise to date, and the accuracies are improved by 78% and 34%, respectively.