  The high polarization observed in the prompt phase of some gamma-ray bursts
(GRBs) arouses extensive studies on the emission mechanism. In this paper, we
investigate the polarization properties of the synchrotron-self-Compton (SSC)
process from a highly relativistic jet. A magnetic-dominated, baryon-loaded jet
ejected from the central engine travels with a large Lorentz factor. Shells
with slightly different velocities collide with each other and produce shocks.
The shocks accelerate electrons to power-law distribution, and at the same
time, magnify the magnetic field. Electrons move in the magnetic field and
produce synchrotron photons. The synchrotron photons suffer from the Compton
scattering (CS) process and then are detected by an observer locating slightly
off-axis. We derive analytically the formulae of photon polarization in the SSC
process in two magnetic configurations: magnetic field in the shock plane and
perpendicular to the shock plane. We show that photons induced by the SSC
process can be highly polarized, with the maximum polarization $\Pi \sim 24\%$
in the energy band $[0.5,5]$ MeV. The polarization depends on the viewing
angles, peaking in the plane perpendicular to the magnetic field. In the energy
band $[0.05,0.5]$ MeV, in which most $\gamma$-ray polarimeters are active, the
polarization is about twice of that in the Thomson limit, reaching to $\Pi\sim
20\%$. This implies that the Klein-Nishina effect, which is often neglected in
literatures, should be carefully considered.
