Context. The presence of magnetic fields in O-type stars has been suspected for a long time. The discovery of these fields would explain a wide range of well documented enigmatic phenomena in massive stars, in particular cyclical wind variability, Ha emission variations, chemical peculiarity, narrow X-ray emission lines, and non-thermal radio/X-ray emission. Aims. To investigate the incidence of magnetic fields in O stars, we acquired 38 new spectropolarimetric observations with FORS 1 (FOcal Reducer low dispersion Spectrograph) mounted on the 8-m Kueyen telescope of the VLT. Methods. Spectropolarimetric observations were obtained at different phases for a sample of 13 O stars. Ten stars were observed in the spectral range 348-589 nm, HD36879 and HD148937 were observed in the spectral region 325-621 nm, and HD155806 was observed in both settings. To prove the feasibility of the FORS1 spectropolarimetric mode for the measurements of magnetic fields in hot stars, we present in addition 12 FORS 1 observations of the mean longitudinal magnetic field in theta(1) OriC and compare them with measurements obtained with the MuSiCoS, ESPaDOnS, and Narval spectropolarimeters. Results. Most stars in our sample, which were observed on different nights, show a change of the magnetic field polarity, but a field at a significance level of 3 sigma was detected in only four stars, HD36879, HD148937, HD152408, and HD164794. The largest longitudinal magnetic field, = -276 +/- 88 G, was detected in the Of?p star HD148937. We conclude that large-scale organized magnetic fields with polar field strengths larger than 1 kG are not widespread among O-type stars.