We discuss the possibility to estimate hadronic matrix elements of gluonic operators in the framework of the QCD sum rule approach and consider in detail the particular example of the gluon form factor of the proton, normalized at Q2=0 to the fraction of the proton momentum carried by gluons. To this end we evaluate the proton coupling to a suitable quark-quark-quark-gluon current and calculate the three-point correlation function of a pair of such currents and the traceless part of the gluonic contribution to the energy-momentum tensor. We obtain a rather slow Q2-dependence of this form factor, which corresponds to the radius of the gluon distribution Rreverse similar, equals0.3−0.35 fm and is much smaller than the electromagnetic radius.