  The X-ray radiation produced on the surface of accreting magnetised neutron
stars is expected to be strongly polarised. A swing of the polarisation vector
with the pulsar phase gives a direct measure of the source inclination and
magnetic obliquity. In the case of rapidly rotating millisecond pulsars, the
relativistic motion of the emission region causes additional rotation of the
polarisation plane. Here, we develop a relativistic rotating vector model,
where we derive analytical expression for the polarisation angle as a function
of the pulsar phase accounting for relativistic aberration and gravitational
light bending in the Schwarzschild metric. We show that in the case of fast
pulsars the rotation of the polarisation plane can reach tens of degrees,
strongly influencing the observed shape of the polarisation angle's phase
dependence. The rotation angle grows nearly linearly with the spin rate but it
is less sensitive to the neutron star radius. Overall, this angle is large even
for large spots. Our results have implications with regard to the modelling of
X-ray polarisation from accreting millisecond pulsars that are to be observed
with the upcoming Imaging X-ray Polarimeter Explorer and the enhanced X-ray
Timing and Polarimetry mission. The X-ray polarisation may improve constraints
on the neutron star mass and radius coming from the pulse profile modelling.
