We report the observation of a particularly simple effect of spin-orbit coupling which allows for efficient manipulation of spins by an electric current in semiconductor nanostructures. Passing an electric current density of j = 2.5 mA/cm through a modulation doped Si quantum well (density of 5 × 1011 cm-2) perpendicular to an in-plane magnetic field, we observe a shift of the spin resonance of the conduction electrons (CESR) by about 0.1 mT. This shift reverses sign when we invert (i) the current direction, (ii) the magnetic field direction and it vanishes for perpendicular magnetic field. We show that this current-induced shift in g-factor, i.e., its dependence on current and carrier density, its temperature dependence and its anisotropy can be consistently and quantitatively explained in terms of the Bychkov-Rashba coefficient determined earlier from the CESR broadening and the g-factor anisotropy . Other sources of magnetic field (e.g. the Oersted effect) are negligible. This effect can be utilized for g-factor tuning, and thus for local spin manipulation: passing a current through some part of a sample may be utilized to bring those electrons into resonance with a microwave field. These spins are thus excited to Rabi oscillations and, using current pulses of suitable duration, π rotations (or by any other angle) can be achieved.