The degree of freedom of spin in quantum systems serves as an unparalleled laboratory where intriguing quantum physical properties can be observed, and the ability to control spin is a powerful tool in physics research. We propose a method for controlling spin in a system of rare isotopes which takes advantage of the mechanism of the projectile fragmentation reaction combined with the momentum-dispersion matching technique. The present method was verified in an experiment at the RIKEN RI Beam Factory, in which a degree of alignment of 8% was achieved for the spin of a rare isotope Al-32. The figure of merit for the present method was found to be greater than that of the conventional method by a factor of more than 50.