The basic theory of relativistic Birkhoffian dynamics of rotational system is constructed,and the Birkhoffian,Birkhoff's functions,Pfaff action,Pfaff-Birkhoff principle,Pfaff-Birkhoff-D'Alembert principle and Birkhoffian equations are given.The relations among relativistic Lagrangian mechanics,Hamiltonian mechanics and relativistic Birkhoffian dynamics of rotational system are studied.It is proved that the holonomic conserved and holonomic non-conserved rotational relativistic systems can all belong to the rotational relativistic Birkhoffian system.