Based on a data sample of 106 M $psi^{prime}$ events collected with the BESIII detector, the decays $psi^{prime}argammachi_{c0, 2}$,$chi_{c0, 2}argammagamma$ are studied to determine the two-photon widths of the $chi_{c0, 2}$ states. The two-photon decay branching fractions are determined to be ${cal B}(chi_{c0}argammagamma) = (2.24pm 0.19pm 0.12pm 0.08)times 10^{-4}$ and ${cal B}(chi_{c2}argammagamma) = (3.21pm 0.18pm 0.17pm 0.13)times 10^{-4}$. From these, the two-photon widths are determined to be $Gamma_{gamma gamma}(chi_{c0}) = (2.33pm0.20pm0.13pm0.17)$ keV, $Gamma_{gamma gamma}(chi_{c2}) = (0.63pm0.04pm0.04pm0.04)$ keV, and $cal R$ $=Gamma_{gamma gamma}(chi_{c2})/Gamma_{gamma gamma}(chi_{c0})=0.271pm 0.029pm 0.013pm 0.027$, where the uncertainties are statistical, systematic, and those from the PDG ${cal B}(psi^{prime}argammachi_{c0,2})$ and $Gamma(chi_{c0,2})$ errors, respectively. The ratio of the two-photon widths for helicity $lambda=0$ and helicity $lambda=2$ components in the decay $chi_{c2}argammagamma$ is measured for the first time to be $f_{0/2} =Gamma^{lambda=0}_{gammagamma}(chi_{c2})/Gamma^{lambda=2}_{gammagamma}(chi_{c2}) = 0.00pm0.02pm0.02$.
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