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Aims. We aim to study the magnetic field in solar spicules using high-resolution spectropolarimetric observations in the Ca II 8542 Å line obtained with the Swedish 1-m Solar Telescope. Methods. The equations that result from the application of the weak field approximation (WFA) to the radiative transfer equations were used to infer the line-of-sight (LOS) component of the magnetic field ( B LOS ). Two restrictive conditions were imposed on the Stokes I and V profiles at each pixel before they could be used in a Bayesian inversion to compute its B LOS . Results. The LOS magnetic field component was inferred in six data sets totalling 448 spectral scans in the Ca II 8542 Å line and containing both active region and quiet Sun areas, with values of hundreds of Gauss being abundantly inferred. There seems to be no difference, from a statistical point of view, between the magnetic field strength of spicules in the quiet Sun or near an active region. On the other hand, the B LOS distributions present smaller values on the disc than off-limb, a fact that can be explained by the effect of superposition on the chromosphere of on-disc structures. We show that on-disc pixels in which the B LOS is determined are possibly associated with spicular structures because these pixels are co-spatial with the magnetic field concentrations at the network boundaries and the sign of their B LOS agrees with that of the underlying photosphere. We find that spicules in the vicinity of a sunspot have a magnetic field polarity (i.e. north or south) equal to that of the sunspot. This paper also contains an analysis of the effect of off-limb overlapping structures on the observed Stokes I and V parameters and the B LOS obtained from the WFA. It is found that this value is equal to or smaller than the largest LOS magnetic field components of the two structures. In addition, using random B LOS , Doppler velocities, and line intensities of these two structures leads in ≃50% of the cases to Stokes I and V parameters that are unsuitable to be used with the WFA. Conclusions. Our results present a scarcity of LOS magnetic field components smaller than some 50 G, which must not be taken as evidence against the existence of these magnetic field strengths in spicules. This fact possibly arises as the consequence of signal superposition and noise in the data. We also suggest that the failure of previous works to infer the strong magnetic fields in spicules detected here is their coarser spatial and/or temporal resolution.