  This paper presents a simple model of polarisation rotation in optically thin
relativistic jets of blazars. The model is based on the development of helical
(kink) mode of current-driven instability. A possible explanation is suggested
for the observational connection between polarisation rotations and
optical/gamma-ray flares in blazars, if the current-driven modes are triggered
by secular increases of the total jet power. The importance of intrinsic
depolarisation in limiting the amplitude of coherent polarisation rotations is
demonstrated. The polarisation rotation amplitude is thus very sensitive to the
viewing angle, which appears to be inconsistent with the observational
estimates of viewing angles in blazars showing polarisation rotations. Overall,
there are serious obstacles to explaining large-amplitude polarisation
rotations in blazars in terms of current-driven kink modes.
