When the Rashba spin orbit interaction is available， the spin polarization along the spin quantization axis is derived form the spin density matrix， with the help of current and shot noise formula based on the scattering theory. Charge shot noise and spin polarization are derived in the case of single channel， and there exists no relation between them. Due to the difficulty in derivation in multichannel， at least two channels， the nonequilibrium Greens function technique is used to numerically compute the scattering matrix， the current and the shot noise of clean two-dimensional electron gas governed by the spin orbit coupling effect. The relation between charge shot noise and spin polarization is investigated separately in conditions of variable bias， spin orbit interaction coefficient and conductor length， which demonstrates that the establishment of quantitive relation may provide a new way to realize all-electrical detection of spin polarization.