Aims. We aim to infer information about the magnetic field in the low solar corona from coronal rain clumps using high-resolution spectropolarimetric observations in the Ca » II 8542 Å line obtained with the Swedish 1 m Solar Telescope. Methods. The weak-field approximation (WFA) provides a simple tool to obtain the line-of-sight component of the magnetic field from spectropolarimetric observations. We adapted a method developed in a previous paper in order to assess the different conditions that must be satisfied in order to properly use the WFA for the data at hand. We also made use of velocity measurements in order to estimate the plane-of-the-sky magnetic field component, so that the magnetic field vector could be inferred. Results. We have inferred the magnetic field vector from a data set totalling 100 spectral scans in the Ca » II 8542 Å line, containing an off-limb view of the lower portion of catastrophically cooled coronal loops in an active region. Our results, albeit limited by the cadence and signal-to-noise ratio of the data, suggest that magnetic field strengths of hundreds of Gauss, even reaching up to 1000 G, are omnipresent at coronal heights below 9 Mm from the visible limb. Our results are also compatible with the presence of larger magnetic field values such as those reported by previous works. However, for large magnetic fields, the Doppler width from coronal rain is not that much larger than the Zeeman width, thwarting the application of the WFA. Furthermore, we have determined the temperature, T, and microturbulent velocity, ζ, of coronal rain clumps and off-limb spicules present in the same data set, and we have found that the former ones have narrower T and ζ distributions, their average temperature is similar, and coronal rain has microturbulent velocities smaller than those of spicules.