  Raman scattering by atomic hydrogen converts the UV continuum around
Ly$\beta$ into optical continuum around H$\alpha$, and the basic atomic physics
has been discussed in several works on symbiotic stars. We propose that the
same process may operate in active galactic nuclei (AGN) and calculate the
linear polarization of the broad emission lines Raman-scattered by a high
column neutral hydrogen compnent. The conversion efficiency of the Raman
scattering process is discussed and the expected scattered flux is computed
using the spectral energy distribution of an AGN given by a typical power law.
The high column H {\sc i} component in AGN is suggested by many observations
encompassing radio through UV and X-ray ranges. When the neutral hydrogen
component with a column density $\sim 10^{22} cm^{-2}$ is present around the
active nucleus, it is found that the scattered H$\alpha$ is characterized by a
very broad width $\sim 20,000 km/s$ and that the strength of the polarized flux
is comparable to that of the electron-scattered flux expected from a
conventional unified model of narrow line AGN. The width of the scattered flux
is mainly determined by the column density of the neutral scatterers where the
total scattering optical depth becomes of order unity. The asymmetry in the
Raman scattering cross section around Ly$\beta$ introduces red asymmetric
polarized profiles around H$\alpha$. The effects of the blended Ly$\beta$ and O
{\sc vi} 1034 doublet are also investigated. We briefly discuss the
spectropolarimetric observations performed on the Seyfert galaxy IRAS
110548-1131 and the narrow line radio galaxy Cyg A.
