Using the scattering approach, shot noise in ferromagnetic/semiconductor/ferromagnetic heterjunctions in the presence of Rashba spin-orbit interaction has been studied theoretically. The quantum size effect, degree of spin-polarization, and Rashba spin-orbit interaction are considered simultaneously. The results indicate that the Fano factors for spin-polarized electrons oscillate strongly due to the influence not only of the Rashba spin-orbit coupling but also of the length of the semiconductor layer. For a certain length of semiconductor, the Fano factors can be determined by the strength of the Rashba spin-orbit coupling. Further, it is found that the higher the degree of spin-polarization, the larger the Fano factors. These results may be useful in the measurement of Rashba spin-orbit coupling via shot noise.