We analyzed the two coupled propagation equations in a circularly birefringent fiber. We found that the difference between perpendicular and parallel Raman gain results in energy transform from a slow to fast circularly polarized component. We have shown this effect analytically and by a numerical simulation. We analyzed and measured the polarization of solitons generated by modulation instability and we found that polarization ellipticity of solitons is distributed randomly; however, the ellipticity of polarization is close to the polarization of the input pulse and always is shifted toward the circular polarization. Therefore, if a circularly polarized pulse is launched at the fiber input then the produced solitons are also circularly polarized. In the experiment, we used SMF-28 twisted fiber by ; the fiber twist mitigated the random linear birefringence, and the fiber was pumped by 1-ns pulse. We have found that circular polarization of the pump pulse in the twisted fiber produces circularly polarized solitons with a high grade of polarization while in the fiber without twist the soliton polarization was random.