We　proposed　a　theoretical　model　to　investigate　the　polarization　pulling　effect　in　bi-directionally　pumped　degenerate　Raman　assisted　fiber　optical　parameter　amplifiers　(RA-FOPAs)　using　randomly　birefringent　fibers.　The　contributions　of　chromatic　dispersion,　polarization　mode　dispersion　(PMD),　Raman　gain,　and　nonlinear　effects　to　the　phase　matching　in　RA-FOPAs　are　investigated.　We　characterize　four　different　states　of　polarization　pulling　in　RA-FOPAs.　We　found　that　broadband　polarization　attraction　can　be　obtained　in　the　optimum　phase-matching　state　of　the　bi-directionally　pumped　RA-FOPAs　when　the　parametric　pump　power　is　chosen　to　avoid　deep　saturation　of　the　Raman　gain.　(C)　2016　Optical　Society　of　America