To investigate if magnetic fields are present in Wolf–Rayet stars, we selected a few stars in the Galaxy and one in the Large Magellanic Cloud (LMC). We acquired low-resolution spectropolarimetric observations with the European Southern Observatory FORS 2 (FOcal Reducer low dispersion Spectrograph) instrument during two different observing runs. During the first run in visitor mode, we observed the LMC Wolf–Rayet star BAT99 7 and the stars WR 6, WR 7, WR 18, and WR 23 in our Galaxy. The second run in service mode was focused on monitoring the star WR 6. Linear polarization was recorded immediately after the observations of circular polarization. During our visitor observing run, the magnetic field for the cyclically variable star WR 6 was measured at a significance level of 3.3σ (〈Bz〉 = 258 ± 78 G). Among the other targets, the highest value for the longitudinal magnetic field, 〈Bz〉 = 327 ± 141 G, was measured in the LMC star BAT99 7. Spectropolarimetric monitoring of the star WR 6 revealed a sinusoidal nature of the 〈Bz〉 variations with the known rotation period of 3.77 d, significantly adding to the confidence in the detection. The presence of the rotation-modulated magnetic variability is also indicated in our frequency periodogram. The reported field magnitude suffers from significant systematic uncertainties at the factor of 2 level, in addition to the quoted statistical uncertainties, owing to the theoretical approach used to characterize it. Linear polarization measurements showed no line effect in the stars, apart from WR 6. BAT99 7, WR 7, and WR 23 do not show variability of the linear polarization over two nights.