  In this paper we calculate the potential sensitivity of the CUORE detector to
axions produced in the Sun through the Primakoff process and detected by the
inverse coherent Bragg-Primakoff process. The conversion rate is calculated
using density functional theory for the electron density and realistic
expectations for the energy resolution and background of CUORE. Monte Carlo
calculations for $5~$y$\times741~$kg=$3705~$kg y of exposure are analyzed using
time correlation of individual events with the theoretical time-dependent
counting rate and lead to an expected limit on the axion-photon coupling
$g_{a\gamma\gamma}<3.83\times 10^{-10}~GeV^{-1}$ for axion masses less than
$100$ eV.
