  Synchrotron radiation and Compton scattering are widely accepted as the most
likely emission mechanisms of some astrophysical phenomena, such as gamma-ray
bursts (GRBs) and active galactic nuclei (AGNs). The measurement on
polarization of photons provides a useful tool to distinguish different
emission mechanisms and structures of the emission region. Based on the
differential cross section of a polarized photon scattered by an unpolarized
electron of any initial momentum, we derive analytical formula of polarization
for beamed photons scattered by isotropic electrons with a power law
distribution. Numerical calculations are carried out in four special cases:
electrons at rest, Thomson limit, head-on collision and monochromatic
electrons. It is found that the maximum polarization can be as high as $100\%$
for low energy photons, if the electrons are at rest. Although polarization is
highly suppressed due to the isotropic electrons, a maximum value of $\sim 10\%
\-- 20\%$ can still be achieved. Compton scattering process can be used to
explain the polarization of GRB 041219A and GRB 100826A.
