We study exclusive dijet production in electron-proton deep inelastic
scattering at a future Electron Ion Collider. We predict the elliptic
modulation of the cross section as a function of the angle between the dijet
transverse momentum and the recoil momentum, and show that this modulation is
due to non-trivial angular correlations between the transverse coordinate and
transverse momentum in the Wigner (or Husimi) distribution. The small-$x$
evolution is shown to decrease the elliptic modulation in the EIC kinematics,
because of the growth of the proton with decreasing $x$.