We address the problem of a relativistic particle in a periodic asymmetric
potential of the ratchet type. As a solid-state realization of such a parti
cle, we consider a single-flux quantum in a long annular Josephson junction
embedded in an inhomogeneous magnetic field. A deterministic (nonthermal)
regime is theoretically investigated and compared with numerical results. T
he ratchet velocity of the relativistic fluxon is found qualitatively diffe
rent from that of a nonrelativistic particle.