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 $\sin(ϕ_q -ϕ_Δ)$, where $ϕ_Δ$ and $ϕ_q$ 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. ; Comment: 8 pages, 2 figures