  To accurately characterize the planets a star may be hosting, stellar
parameters must first be well-determined. $\tau$ Ceti is a nearby solar analog
and often a target for exoplanet searches. Uncertainties in the observed
rotational velocities have made constraining $\tau$ Ceti's inclination
difficult. For planet candidates from radial velocity (RV) observations, this
leads to substantial uncertainties in the planetary masses, as only the minimum
mass ($m \sin i$) can be constrained with RV. In this paper, we used new
long-baseline optical interferometric data from the CHARA Array with the MIRC-X
beam combiner and extreme precision spectroscopic data from the Lowell
Discovery Telescope with EXPRES to improve constraints on the stellar
parameters of $\tau$ Ceti. Additional archival data were obtained from a
Tennessee State University Automatic Photometric Telescope and the Mount Wilson
Observatory HK project. These new and archival data sets led to improved
stellar parameter determinations, including a limb-darkened angular diameter of
$2.019 \pm 0.012$ mas and rotation period of $46 \pm 4$ days. By combining
parameters from our data sets, we obtained an estimate for the stellar
inclination of $7\pm7^\circ$. This nearly-pole-on orientation has implications
for the previously-reported exoplanets. An analysis of the system dynamics
suggests that the planetary architecture described by Feng et al. (2017) may
not retain long-term stability for low orbital inclinations. Additionally, the
inclination of $\tau$ Ceti reveals a misalignment between the inclinations of
the stellar rotation axis and the previously-measured debris disk rotation axis
($i_\mathrm{disk} = 35 \pm 10^\circ$).
