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Background: The $^{12}{\rm C}(\alpha,\gamma)^{16}$O reaction, determining thesurvival of carbon in red giants, is of interest for nuclear reaction theoryand nuclear astrophysics. Numerous attempts to obtain the astrophysical factorof the $^{12}{\rm C}(\alpha,\gamma)^{16}$O reaction, both experimental andtheoretical, have been made for almost 50 years. The specifics of the $^{16}$Onuclear structure is the presence of two subthreshold bound states, (6.92 MeV,2$^+$) and (7.12 MeV, 1$^-$), dominating the behavior of the low-energy$S$-factor. The strength of these subthreshold states is determined by theirasymptotic normalization coefficients (ANCs) which need to be known with highaccuracy. Recently, using the model-independent extrapolation method,Blokhintsev {\it et al.} [Eur. Phys. J. A {\bf 59}, 162 (2023)] determined theANCs for the three subthreshold states in $^{16}$O.  Purpose: In this paper, using these newly determined ANCs, we calculated thelow-energy astrophysical $S$-factors for the $^{12}{\rmC}(\alpha,\gamma)^{16}$O radiative capture.  Method: The $S$-factors are calculated within the framework of the $R$-matrixmethod using the AZURE2 code.  Conclusion: Our total $S$-factor includes the resonance $E1$ and $E2$transitions to the ground state of $^{16}$O interfering with the correspondingdirect captures and cascade radiative captures to the ground state of $^{16}$Othrough four subthreshold states: $0_2^+,\,3^-,\, 2^+$ and $1^-$. Since ourANCs are higher than those used by deBoer {\it et al.} [Rev. Mod. Phys. {\bf89}, 035007 (2017)], the present total $S$-factor at the most effectiveastrophysical energy of 300 keV is 174 keVb versus 137 keVb of that work.Accordingly, our calculated reaction rate at low temperatures ($T_{9} < 2$) ishigher than the one given in the aforesaid paper.

New ANCs for $\alpha + {}^{12}{\rm C}$ synthesis obtained using  extrapolation method and the $S$-factor for ${}^{12}{\rm  C}(\alpha,\gamma){}^{16}{\rm O}$ radiative capture