  We investigated the Rashba spin splittings in a compressive-strained
SrTiO$_3$(001) ultra thin-film using first-principles calculations. The effect
of the polarization due to the compressive strain leads to the 2DEG with large
Rashba spin splittings, where the sheet carrier density is of the same order of
magnitude as that of the heterostructure LaAlO$_3$/SrTiO$_3$ ($\sim10^{14}$
cm$^{-2}$). Some localized surface states (SSs) show the giant Rashba
coefficient $\alpha_R$ larger than 100 meV$\cdot$\AA.
