We electrically detect charge current induced spin polarization on the surface of molecular beam epitaxy grown Bi$_2$Te$_3$ thin film in a two-terminal device with a ferromagnetic MgO/Fe and a nonmagnetic Ti/Au contact. The two-point resistance, measured in an applied magnetic field, shows a hysteresis tracking the magnetization of the Fe. A theoretical estimate is obtained for the change in resistance on reversing the magnetization direction of Fe from coupled spin-charge transport equations based on quantum kinetic theory. The order of magnitude and the sign of the hysteresis is consistent with spin-polarized surface state of Bi$_2$Te$_3$.
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