A Swept Source Polarization-Sensitive Optical Coherence Tomography (SS-PS-OCT) instrument has been designed, constructed, and verified to provide high sensitivity depth-resolved birefringence and phase retardation measurements of the retinal nerve fiber layer. The swept-source laser had a center wavelength of 1059 nm, a full-width-half-max spectral bandwidth of 58 nm and an A-line scan rate of 34 KHz. Power incident on the cornea was 440 µW and measured axial resolution was 17 µm in air. A multiple polarization state nonlinear fitting algorithm was used to measure retinal birefringence with low uncertainty. Maps of RNFL phase retardation in a subject measured with SS-PS-OCT compare well with those generated using a commercial scanning laser polarimetry instrument. Peak-to-valley variation of RNFL birefringence given here is less than values previously reported at 840nm.