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Transition-metal dichalcogenides such as WSe2 and MoS2 have electronic band structures that are ideal for hosting many exotic spin-orbit phenomena. Here we investigate the possibility to generate and modulate a giant Zeeman-type spin polarization in WSe2 under an external electric field. By tuning the perpendicular electric field applied to the WSe2 channel with an electric-double-layer transistor, we observe a systematic crossover from weak localization to weak anti-localization in magnetotransport. Our optical reflection measurements also reveal an electrically tunable exciton splitting. Using first-principles calculations, we propose that these are probably due to the emergence of a merely out-of-plane and momentum-independent spin splitting at and in the vicinity of the vertices of the WSe2 Brillouin zone under electric field. The non-magnetic approach for creating such an intriguing spin splitting keeps the system time-reversally invariant, thereby suggesting a new method for manipulating the spin degrees of freedom of electrons. [ABSTRACT FROM AUTHOR]