  Constraining the polarisation properties of extragalactic point sources is a
relevant task not only because they are one of the main contaminants for
primordial cosmic microwave background B-mode detection if the tensor-to-scalar
ratio is lower than r = 0.001, but also for a better understanding of the
properties of radio-loud active galactic nuclei. We develop and train a machine
learning model based on a convolutional neural network to learn how to estimate
the polarisation flux density and angle of point sources embedded in cosmic
microwave background images knowing only their positions. To train the neural
network, we use realistic simulations of patches of area 32x32 pixels at the
217 GHz Planck channel with injected point sources at their centres. The
patches also contain a realistic background composed by dust, the CMB and
instrumental noise. Firstly, we study the comparison between true and estimated
polarisation flux densities for P, Q and U. Secondly, we analyse the comparison
between true and estimated polarisation angles. Finally, we study the
performance of our model with real data and we compare our results against the
PCCS2. We obtain that our model is reliable to constrain the polarisation flux
above 80 mJy. For this limit, we obtain errors lower than 30%. Training the
same network with Q and U, the reliability limit is above +-250 mJy for
determining the polarisation angle of both Q and U sources with a 1sigma
uncertainty of +-29deg and +-32deg for Q and U sources respectively. We obtain
similar results to the PCCS2 for some sources, although we also find
discrepancies in the 300-400 mJy flux density range with respect to the Planck
catalogue. Based on these results, our model seems to be a promising tool to
give estimations of the polarisation flux densities and angles of point sources
above 80 mJy in any catalogue with practically null computational time.
