Spontaneous spin polarization of the electrical current flowing through nonmagnetic semiconductor junctions can be generated by carrier scattering processes that are independent of the carrier spin. The two required elements for current-induced spin polarization are (1) the presence of built-in spatially-varying electric fields in the junction and (2) energy-dependent carrier scattering processes. Spin-orbit interactions are not required for this effect, thus it should occur in materials like silicon that lack significant spin-orbit interactions. Approximate analytic expressions as well as detailed numerical simulations of the time-dependent nonlinear spin transport in a GaAs junction strongly suggest that the recent experimental observation of current-induced spin polarization in this system [Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Phys. Rev. Lett. 93, 176601 (2004)] may be explained by this effect.