We analyse the recently observed effect of an in-plane electric current through a Si quantum well on the conduction electron spin resonance. We find that the ratio of resonance shift and current density is independent of temperature and dissipation processes, but the channel current is reduced due to a parallel electric channel in heavily modulation doped samples. The inhomogeneous current distribution results in some broadening of the ESR line width. In high mobility Si/SiGe layers the current induced increase in the electron temperature is considerably larger than the increase in the lattice temperature. The signal amplitude scales with the square of electron mobility.