  Recent quasar microlensing observations have constrained the X-ray emission
sizes of quasars to be about 10 gravitational radii, one order of magnitude
smaller than the optical emission sizes. Using a new ray-tracing code for the
Kerr space-time, we find that the observed X-ray flux is strongly influenced by
the gravity field of the central black hole, even for observers at moderate
inclination angles. We calculate inclination-dependent flux profiles of active
galactic nuclei in the optical and X-ray bands by combining the Kerr lensing
and projection effects for future references. We further study the dependence
of the X-ray-to-optical flux ratio on the inclination angle caused by
differential lensing distortion of the X-ray and optical emission, assuming
several corona geometries. The strong lensing X-ray-to-optical magnification
ratio can change by a factor of ~10 for normal quasars in some cases, and
another factor of ~10 for broad absorption line quasars (BALs) and obscured
quasars. Comparing our results with the observed distributions in normal and
broad absorption line quasars, we find that the inclination angle dependence of
the magnification ratios can change the X-ray-to-optical flux ratio
distributions significantly. In particular, the mean value of the spectrum
slope parameter $\alpha_{ox},$ $0.3838\log F_{2 keV}/F_{2500 {\AA}}$, can
differ by ~0.1-0.2 between normal and broad absorption line quasars, depending
on corona geometries, suggesting larger intrinsic absorptions in BALs.
