Aims: We present a polarimetric and spectroscopic study of the persistent ultra-compact X-ray binary 4U 0614+091 aimed at searching for the emission of a relativistic particle jet and at unveiling the orbital period Porb of the system. Methods: We obtained r-band polarimetric observations with the Telescopio Nazionale Galileo (TNG) equipped with the PAOLO polarimeter and with the Nordic Optical Telescope (NOT) equipped with the ALFOSC instrument, covering ~2 h and ~0.5 h observations, respectively. We carried out low resolution spectroscopy of the system using the ESO Very Large Telescope equipped with FORS1 for ~1.5 h (16 spectra covering the range 4300-8000 Å). Results: The polarimetric analysis performed starting from the TNG dataset revealed a polarisation degree in the r-band of 3% ± 1%. From the NOT dataset, due to the lower signal-to-noise ratio, we could obtain only a 3σ upper limit of 3.4%. From the joining of a spectroscopic and photometric analysis, through the study of the equivalent width variations of the CII 7240 Å line and the r-band light curve, we could find a hint of a ~45 min periodicity. Conclusions: A polarisation degree P of ~3% in the r-band is consistent with the emission of a relativistic particle jet, which is supposed to emit intrinsically linearly polarised synchrotron radiation. Since no variations of P with time have been detected, and the accretion disc of the system does not contain ionised hydrogen, scattering by free electrons in the accretion disc has been rejected. The period of ~45 min obtained through the analysis of the system light curve and of the equivalent width variations of the selected spectral line is probably linked to the presence of a hot spot or a superhump in the accretion disc, and lead to an orbital period ≳1 h for the binary system. Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofísica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias and with the Nordic Optical Telescope, operated by the Nordic Optical Telescope Scientific Association at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofísica de Canarias and on observations made with ESO Telescopes at the Paranal Observatory under programme ID 079.D-0884(A).Spectra and polametric observations are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/572/A99