This paper presents an analytical solution for an orthotropic circular cross section bar with a magnetic coating weakened by multiple arbitrary oriented cracks under Saint-Venant torsion by means of the distributed dislocation technique. At first, the solution of the orthotropic bar with a magnetic coating weakened by a Volterra-type screw dislocation is achieved with the aid of the finite Fourier sine transform. Next, the problem is then reduced to a set of singular integral equations with a Cauchy type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Finally, several examples are solved and numerical results are discussed to reveal the effect of the magnetic layer on the reduction of the mechanical stress intensity factor in the bar.