Asymmetry of p(->)+p(->)->gamma+jet+X process and problem of Delta G

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.