The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles, a symplectic two-form which is a matrix in spin indices is proposed. The particle number and current densities for the Dirac particles are acquired in the helicity basis. Following a similar procedure, the semiclassical kinetic theory of the Weyl particles is accomplished. It is shown that the phase-space dynamics of the Weyl and Dirac particles is directly linked. The anomalous chiral effects due to the external electromagnetic fields and angular velocity of the frame are calculated.