The interaction between random birefringence and the Kerr effect is investigated numerically with dispersion-managed (DM) solitons. In zero-averaged-path DM optical fiber links, because linear dispersion is fully compensated, the Kerr effect becomes a detrimental residual factor to the transmission of DM soliton and results in a narrower optical pulse. However, under the proper conditions, an optical pulse can propagate better through the balance between random birefringence and the Kerr effect. After optimally mapping the optical pulse power and birefringence parameter of an optical fiber, the polarization-mode dispersion resulting from random birefringence can essentially be balanced by the Kerr effect. In addition, considering polarization-dependent losses, we find that the pulse width's fluctuation and broadening are very large even with little loss difference in the two polarization components.