  In this paper we show that the $\gamma+$jet invariant mass distribution in
proton-proton collisions at the LHC is significantly sensitive to the quarks
chromoelectric ($\kappa$) and chromomagnetic ($\tilde{\kappa}$) dipole moments.
It is shown that the presence of $\kappa$ or $\tilde{\kappa}$ leads to an
increment of the cross section of $\gamma+$jet process in particular in the
tail of $\gamma+$jet invariant mass distribution. Using the measured
$\gamma+$jet invariant mass distribution by the CMS experiment at the
center-of-mass energy of 8 TeV, we derive bounds on the quarks chromoelectric
and chromomagnetic dipole moments. In extraction of the limits, we consider
both theoretical and systematic uncertainties. The uncertainties originating
from variation of the renomalization/factorization scales and the choice of
proton parton distribution functions are taken into account as a function of
the $\gamma+$jet invariant mass. We exclude $\kappa$ or $\tilde{\kappa}$ above
$10^{-5}$ at 95$\%$ confidence level. This is the most stringent direct upper
limit on $\kappa$ or $\tilde{\kappa}$.
