  Applying the connection between the parton Wigner distribution and orbital
angular momentum (OAM), we investigate the probe of the gluon OAM in hard
scattering processes at the planned electron-ion collider. We show that the
single longitudinal target-spin asymmetry in the hard diffractive dijet
production is very sensitive to the gluon OAM distribution. The associated spin
asymmetry leads to a characteristic azimuthal angular correlation of
$\sin(\phi_q -\phi_\Delta)$, where $\phi_\Delta$ and $\phi_q$ are the azimuthal
angles of the proton momentum transfer and the relative transverse momentum
between the quark-antiquark pair. This study will enable a first measurement of
the gluon OAM in the proton spin sum rule.
