We propose and demonstrate theoretically that resonant inelastic scattering (RIS) can play an important role in dc spin current generation. The RIS makes it possible to generate dc spin current via a simple gate configuration: a single finger gate that locates atop and orients transversely to a quantum channel in the presence of Rashba spin-orbit interaction. The ac-biased finger gate gives rise to a time variation in the Rashba coupling parameter, which causes spin-resolved RIS and, subsequently, contributes to the dc spin current. The spin current depends on both the static and the dynamic parts in the Rashba coupling parameter, ${\ensuremath{\alpha}}_{0}$ and ${\ensuremath{\alpha}}_{1}$, respectively, and is proportional to ${\ensuremath{\alpha}}_{0}{\ensuremath{\alpha}}_{1}^{2}$. The proposed gate configuration has the added advantage that no dc charge current is generated. Our study also shows that the spin current generation can be enhanced significantly in a double finger-gate configuration.