  We study the effect of anisotropic radiation illumination on the alignment of
polycyclic aromatic hydrocarbons (PAHs) and report that cross-sectional
mechanism of alignment earlier considered in terms of gas-grain interactions
can also be efficient for the photon-grain interaction. We demonstrate this by
first calculating the angle-dependence rotational damping and excitation
coefficients by photon absorption followed by infrared emission. We then
calculate the degree of PAH alignment for the different environments and
physical parameters, including the illumination direction, ionization fraction,
and magnetic field strength. For the reflection nebula (RN) conditions with
unidirectional radiation field, we find that the degree of alignment tends to
increase with increasing the angle $\psi$ between the illumination direction
and the magnetic field, as a result of the decrease of the cross-section of
photon absorption with $\psi$. We calculate the polarization of spinning PAH
emission using the obtained degree of alignment for the different physical
parameters, assuming constant grain temperatures. We find that the polarization
of spinning PAH emission from RN can be large, between $5-20~\%$ at frequencies
$\nu > 20$ GHz, whereas the polarization is less than $3~\%$ for
photodissociation regions (PDRs). In realistic conditions, the polarization is
expected to be lower due to grain temperature fluctuations and magnetic field
geometry. The polarization for the diffuse cold neutral medium (CNM) is rather
low, below $1~\%$ at $\nu>20$ GHz, consistent with observations by WMAP and
Planck. Our results demonstrate that the RNe are the favored environment to
observe the polarization of spinning dust emission as well as polarized mid-IR
emission from PAHs.
