  The gamma +jet production in p(->)-p(->) collisions at high energies is
studied. Double-spin asymmetry A{LL} of the process is calculated by using
Monte Carlo code SPHINX. The predictions for A{LL} of the gamma +jet production
in the p(->)-p(->) collisions using the spin-dependent gluon distributions with
positive and negative sign of $\Delta G(x,Q^2)$ are made at RHIC energies. A
possibility to extract the spin-dependent gluon distributions Delta G at STAR
experiment and to discriminate between different theoretical scenarios is
discussed.
