  Angular momentum projection is used to obtain eigen states of angular
momentum from general wave functions. Multi-configuration mixing calculation
with angular momentum projection is an important microscopic method in nuclear
physics. For accurate multi-configuration mixing calculation with angular
momentum projection, concentrated distribution of $z$ components $K$ of angular
momentum in the body-fixed frame ($K$-distribution) is favored. Orientation of
wave functions strongly affects $K$-distribution. Minimization of variance of
$\hat{J}_z$ is proposed as an alignment method to obtain wave functions that
have concentrated $K$-distribution. Benchmark calculations are performed for
$\alpha$-$^{24}$Mg cluster structure, triaxially superdeformed states in
$^{40}$Ar, and Hartree-Fock states of some nuclei. The proposed alignment
method is useful and works well for various wave functions to obtain
concentrated $K$-distribution.
