  Based on the deformed nucleon distributions obtained from the constrained
Skyrme-Hartree-Fock-Bogolyubov calculation using different nuclear symmetry
energies, we have investigated the effects of the neutron skin and the
collision geometry on the yield of free spectator nucleons as well as the yield
ratio $N_n/N_p$ of free spectator neutrons to protons in collisions of deformed
nuclei at RHIC energies. We found that tip-tip (body-body) collisions with
prolate (oblate) nuclei lead to fewest free spectator nucleons, compared to
other collision configurations. While the $N_n/N_p$ ratio is sensitive to the
average neutron-skin thickness of colliding nuclei and the symmetry energy, it
is affected by the polar angular distribution of the neutron skin in different
collision configurations. We also found that the collision geometry effect can
be as large as 50% the symmetry energy effect in some collision systems. Due to
the particular deformed neutron skin in $^{238}$U and $^{96}$Zr, the symmetry
energy effect on the $N_n/N_p$ ratio is enhanced in tip-tip $^{238}$U+$^{238}$U
collisions and body-body $^{96}$Zr+$^{96}$Zr collisions compared to other
collision orientations in the same collision system. Our study may shed light
on probing deformed neutron skin by selecting desired configurations in
high-energy collisions with deformed nuclei.
