We present high-resolution polarimetric observations and low-noise int
egrated profiles of the relativistic binary radio pulsar B1534+12. Rou
ghly 20% of the main pulse emission is linearly polarized at 430 MHz.
Our measurements are sensitive to low-level off-pulse emission and tra
ce the variation in polarization angle through a substantial fraction
of the pulse period. Within the rotating-vector model, two distinct se
ts of geometric parameters fit the data reasonably well. Both geometri
es imply that the pulsar is nearly an orthogonal rotator. We use this
information to select one of the two equally likely values of orbital
inclination obtained separately, from pulse timing measurements, and f
ind that the misalignment between spin and orbital angular momentum is
probably small. In addition to establishing the geometry of the syste
m and providing clues to the relevant emission physics, our results fo
rm a pulse polarization template against which future observations can
be compared in order to constrain or detect relativistic precession o
f the pulsar's spin axis.