We study the effect of anisotropic radiation illumination on the alignment of polycyclic aromatic hydrocarbons (PAHs) and report that the 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 angle ψ between the illumination direction and the magnetic field, as a result of the decrease of the cross section of photon absorption with ψ. 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 RNe can be large, between 5% and 20% at frequencies ν > 20 GHz, whereas the polarization is less than 3% for photodissociation regions. In realistic conditions, the polarization is expected to be lower owing to grain temperature fluctuations and magnetic field geometry. The polarization for the diffuse cold neutral medium is rather low, below 1% at ν > 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 and polarized mid-IR emission from PAHs.