Context. Narrow-line Seyfert 1 galaxies (NLSy1s) constitute the active galactic nuclei subclass associated with systematically lower black hole masses. A few radio-loud NLSy1s have been detected in MeV-GeV energy bands by Fermi, and evidence that blazar-like jets are operating also in radio-loud NLSy1s, has been accumulated. Aims. We wish to quantify the temporal behaviour of the optical polarisation, fraction, and angle for a selected sample of radio-loud NLSy1s. We also search for rotations of the polarisation plane similar to those commonly observed in blazars. Methods. We have conducted R-band optical linear polarisation monitoring of a sample of ten radio-loud NLSy1 galaxies; five of them have previously been detected by Fermi. The dataset obtained with our pivoting instrument, the RoboPol polarimeter of the Skinakas observatory, has been complemented with observations from the KANATA, Perkins, and Steward observatories. When evidence for long rotations of the polarisation plane was found (at least three consecutive measurements covering at least 90°), we carried out numerical simulations to assess the probability that they are caused by intrinsically evolving electric vector position angles (EVPAs) instead of observational noise. Results. Even our moderately sampled sources show clear indications of variability in both polarisation fraction and angle. For the four best-sampled objects in our sample we find multiple periods of significant polarisation angle variability. Several of these events qualify as long rotations. In the two best-sampled cases, namely J1505+0326 and J0324+3410, we find indications for three long rotations of the polarisation angle. We show that although noise can induce the observed behaviour, it is much more likely that the apparent rotation is indeed caused by intrinsic evolution of the EVPA. To our knowledge, this is the very first detection of such events in this class of sources. In the largest dataset (J0324+3410), we find that the EVPA concentrates around a direction that is at 49.3° to the 15 GHz radio jet, implying a projected magnetic field at an angle of 40.7° to that axis. Conclusions. We assess the probability that pure measurement uncertainties are the reason behind the observed long rotations of the polarisation plane. We conclude that although this is not improbable, it is much more likely that intrinsic rotations are responsible for the observed phenomenology. We conclude, however, that much better sampled and larger datasets of larger source samples are necessary to constrain the physical mechanism(s) that generate long EVPA rotations in NLSy1s.