The quark-gluon plasma (QGP) generated in high-energy heavy-ion collisions is the most vortical system human ever made. The orbital angular momentum of the system will be converted into spin polarization of quarks during the evolution of the QGP. In this work, we use a matrix-valued distribution function for massive spin-1/2 fermions. The diagonal part of this distribution is the particle number density and the remaining parts are spin polarization density in the rest frame. From the Kadanoff-Baym equation, we derive Boltzmann equations for the matrix-valued distribution function, where nonlocal collision terms appear at next-to-leading order in space-time gradient. The nonlocal terms contribute as sources for the spin polarization part of the matrix-valued distribution function. The Boltzmann equations we obtained pave the way for numerically simulating spin-transport processes involving spin-vorticity coupling.