The Advanced Solar Coronal Explorer (ASCE) is a mid-explorer (MidEx) mission selected, together with other five, for the a Phase A Concept Study in the 1999 round of MidEX proposal. ASCE's spacecraft bus is a SPARTAN 400 reusable carrier deployed in low Earth orbit by the Space Shuttle. ASCE's payload comprises two instrument modules, the Spectroscopic and Polarimetric Coronagraph (SPC) and the Extreme Ultraviolet Imager (EUVI). The scientific objective of the mission is the investigation, through spectroscopic and polarimetric techniques, of the physics of the coronal heating and of the solar wind acceleration. A critical physical parameter of the corona is the magnetic field. Polarimetric measurements of UV coronal radiation and their interpretation through the Hanle effect can be used for coronal magnetic field diagnostics. One of the SPC spectrometers, the Spectroscopy/Polarimetry channel (SPCH), includes a reflecting Brewster-angle polarimeter for measurements of the linear polarization of the HI Lyman series lines (i.e., Ly-(alpha) , -(beta) , and (gamma) ) and of the O VI 1032 Angstrom line. In this paper, the optical design of the SPCH polarimeter is described. A relevant element of this design is the external occulter (EXO) that is supported on a boom, which is extended 10 m beyond the instrument aperture, once the instrument is in station. The analysis of the stray- light reduction provided by this occulting system is described in this paper. The principal source of stray light is solar disk light that is diffracted from the edge of the EXO and scattered from the telescope mirror. The analysis shows that the stray-light is less than 10-2 the coronal signal. This level of stray-light rejection minimizes the polarized stray light that may be introduced by the EXO's straight edge. The most appropriate material for the polarizer has been found to be CaF2. The material selection criteria are described. Finally, the paper illustrates with an example that if the linear polarization can be measured better than 1%, then the instrumental sensitivity to magnetic fields may reach a few gauss (greater than 2 gauss), in coronal active regions.