  We consider the dynamics of a quantum particle held in a lattice potential,
and subjected to a time-dependent spin-orbit coupling. Tilting the lattice
causes the particle to perform Bloch oscillations, and by suitably changing the
Rashba interaction during its motion, the spin of the particle can be gradually
rotated. Even if the Rashba coupling can only be altered by a small amount,
large spin-rotations can be obtained by accumulating the rotation from
successive oscillations. We show how the time-dependence of the spin-orbit
coupling can be chosen to maximize the rotation per cycle, and thus how this
method can be used to produce a precise and controllable spin-rotator, the
Bloch-Rashba rotator, without requiring an applied magnetic field.
