We show that the relativistic two-stream instability can naturally generate strong magnetic fields with 1e-5 - 1e-1 of the equipartition energy density, in the collisionless shocks of Gamma-Ray-Burst (GRB) sources. The generated fields are parallel to the shock front and fluctuate on the very short scale of the plasma skin depth. The synchrotron radiation emitted from the limb-brightened source image is linearly polarized in the radial direction relative to the source center. Although the net polarization vanishes under circular symmetry, GRB sources should exhibit polarization scintillations as their radio afterglow radiation gets scattered by the Galactic interstellar medium. Detection of polarization scintillations could therefore test the above mechanism for magnetic field generation.

12 pages, 2 figures included. Submitted to ApJ