  We present Very Long Baseline Array polarimetric observations of the
innermost jet of 3C$\sim$84 (NGC$\sim$1275) at 43$\sim$GHz. A significant
polarized emission is detected at the hotspot of the innermost re-started jet,
which is located $\sim$1 pc south from the radio core. While the previous
report presented a hotspot at the southern end of the western limb, the hotspot
location has been moved to the southern end of the eastern limb. Faraday
rotation is detected within an entire bandwidth of the 43-GHz band. The
measured rotation measure (RM) is at most
(6.3$\pm$1.9)$\times10^{5}$$\sim$rad$\sim$m$^{-2}$ and might be slightly time
variable on the timescale of a month by a factor of a few. Our measured RM and
the RM previously reported by the CARMA and SMA observations cannot be
consistently explained by the spherical accretion flow with a power-law
profile. We propose that a clumpy/inhomogeneous ambient medium is responsible
for the observed rotation measure. Using equipartition magnetic field, we
derive the electron density of $2\times10^{4}$$\sim$cm$^{-3}$. Such an electron
density is consistent with the cloud of narrow line emission region around the
central engine. We also discuss the magnetic field configuration from black
hole scale to pc scale and the origin of low polarization.
