  We study Compton scattering, gamma e -> gamma e, in the context of the recent
proposal for Weak Scale Quantum Gravity (WSQG) with large extra dimensions. It
is shown that, with an ultraviolet cutoff $M_S \sim 1$ TeV for the effective
gravity theory, the cross section for this process at the Next Linear Collider
(NLC) deviates from the prediction of the Standard Model significantly. Our
results suggest that, for typical proposed NLC energies and luminosities, WSQG
can be tested in the range 4 TeV$\lsim M_S \lsim$ 16 TeV, making gamma e ->
gamma e an important test channel.
