We have set up an atomic beam of cesium for the study of spin-dependent electron-cesium scattering. The beam is produced by an effusive oven with continuous recirculation of the condensed metal. The beam is optically pumped by circularly polarized light from two laser diodes tuned to the 6(2)S1/2(F = 3) --> 6(2)P3/2(F' = 4) and 6(2)S1/2(F = 4) --> 6(2)P3/2(F' = 5) transitions, respectively. Nearly all atoms are transferred into the F = 4, m(F) = +4 or m(F) = -4 Zeeman level of the ground state, depending on the sense of circular polarization of the pumping light. The population distribution in the optically pumped beam is analyzed in terms of the m(J) = - 1/2 and m(J) = + 1/2 components with a Stern-Gerlach magnet. We find the atomic polarization to be very close to unity at a density of 8 x 10(8) atoms/cm3 in the scattering center. The polarization decreases slightly with increasing density of the cesium beam due to radiation trapping. A spin flipper serves as a means of polarization reversal, introducing no systematic errors in the spin asymmetry measurements. Lock-in technique is used to stabilize the atomic beam polarization by detecting fluorescence light signals.