  We present the first optical polarimetric study of the two transitional
pulsars PSR J1023+0038 and XSS J12270-4859. This work is focused on the search
for intrinsical linear polarisation (LP) in the optical emission from the two
systems. We carried out multiband optical and NIR photo-polarimetry of the two
systems using the ESO NTT at La Silla (Chile), equipped with the EFOSC2 and the
SOFI instruments. XSS J12270-4859 was observed during its radio-pulsar state;
we did not detect LP in all bands, with 3 sigma upper limits of, e.g., 1.4% in
the R-band. We built the NIR-optical averaged spectral energy distribution
(SED) of the system, that could be well described by an irradiated black body
with radius $R_{*} = 0.33\pm0.03\,R_{\odot}$ and albedo $\eta=0.32\pm0.05$,
without the need of further components (thus excluding the visible presence of
an extended accretion disc and/or of relativistic jets). The case was different
for PSR J1023+0038, that was in its accretion phase during our campaign. We
measured a LP of $1.09\pm0.27\%$ and $0.90\pm 0.17\%$ in the V and R bands,
respectively. The phase-resolved polarimetric curve of the source in the R-band
reveals a hint of a sinusoidal modulation at the source 4.75 hr orbital period,
peaked at the same orbital phase as the light curve. The measured LP of PSR
J1023+0038 could in principle be interpreted as scattering with free electrons
(that can be found in the accretion disc of the system or even in the hot
corona that surrounds the disc itself) or to synchrotron emission from a
relativistic particles jet or outflow. However, the NIR-optical SED of the
system built starting from our dataset did not suggest the presence of a jet.
We conclude that the optical LP observed for PSR J1023+0038 is possibly due to
Thomson scattering with electrons in the disc, as also suggested from the
possible modulation of the R-band LP at the system orbital period.
