On the basis of the Landauer-Büttiker scattering formalism and transfer matrix method, we investigate the spin-dependent shot noise properties of electrons tunneling through AlGaAs/GaAs double-barrier heterostructures (DB) sandwiched between two ferromagnets (F) with different relative magnetization direction in the presence of the Rashba spin-orbit interaction and an electric field. The results indicate that the current and shot noise are periodic function of the well width. The phasic difference of the current and shot noise with different spin orientations markedly increase as the barrier thickness increases. As compared with the spin-up electron, the variation of barrier thickness has a higher effect on the current and shot noise of spin-down electron. The oscillation frequencies of the current and shot noise increase with the increase of the Rashba spin-orbit coupling strength. As the external bias voltage increases, the oscillation frequencies of the current and shot noise decrease, and the peak-to-valley ratio and peaks of the current and shot noise increase. The variation of the current and shot noise with increasing spin-orbit coupling strength as well as with increasing bias voltage is strongly dependent on the relative orientation of the two magnetizations in the left and right ferromagnets.