  An alternating electric field, applied to a quantum dot, couples to the
electron spin via the spin-orbit interaction. We analyze different types of
spin-orbit coupling known in the literature and find two efficient mechanisms
of spin control in quantum dots. The linear in momentum Dresselhaus and Rashba
spin-orbit couplings give rise to a fully transverse effective magnetic field
in the presence of a Zeeman splitting at lowest order in the spin-orbit
interaction. The cubic in momentum Dresselhaus terms are efficient in a quantum
dot with non-harmonic confining potential and give rise to a spin-electric
coupling proportional to the orbital magnetic field. We derive an effective
spin Hamiltonian, which can be used to implement spin manipulation on a
timescale of $10 {\rm ns}$ with the current experimental setups.
