  Background: Understanding nuclear shape is a crucial problem in nuclear
physics. In particular, determining the sign of quadrupole deformation, i.e.,
whether prolate or oblate, remains a challenging problem. Purpose: Our aim is
to propose a method for determining the sign of quadrupole deformation using
$\alpha$ inelastic scattering data and to demonstrate its effectiveness.
Method: Our approach is the standard coupled-channel method based on the
macroscopic model. We utilize the nuclear reorientation effect, a phenomenon
associated with the self coupling of excited states, as a probe sensitive to
the sign of deformation. Results: We first provide an overview of how the
reorientation effect influences inelastic scattering cross sections, and
numerically confirm its validity in realistic cases. We then demonstrate that
the sign of deformation can be uniquely determined from inelastic scattering
cross section data. Conclusion: Our technique offers a systematic approach for
determining the sign of deformation in both stable and unstable nuclei. The
broad applicability of $\alpha$ inelastic scattering will make it a valuable
tool to study shape of nuclei, especially unstable nuclei.
