  We propose a novel observable for the experimental detection of the gluon
orbital angular momentum (OAM) that constitutes the proton spin sum rule. We
consider longitudinal double spin asymmetry in exclusive dijet production in
electron-proton scattering and demonstrate that the $\cos \phi$ azimuthal angle
correlation between the scattered electron and proton is a sensitive probe of
the gluon OAM at small-$x$ and its interplay with the gluon helicity. We also
present a numerical estimate of the cross section for the kinematics of the
Electron-Ion Collider.
