Tunable polarization over a wide spectral range is a required feature of
light sources employed to investigate the properties of local symmetry in both
condensed and low-density matter. Among new-generation sources, free-electron
lasers possess a unique combination of very attractive features, as they allow
to generate powerful and coherent ultra-short optical pulses in the VUV and
X-ray spectral range. However, the question remains open about the possibility
to freely vary the light polarization of a free-electron laser, when the latter
is operated in the so-called nonlinear harmonic-generation regime. In such
configuration, one collects the harmonics of the free-electron laser
fundamental emission, gaining access to the shortest possible wavelengths the
device can generate. In this letter we provide the first experimental
characterization of the polarization of the harmonic light produced by a
free-electron laser and we demonstrate a method to obtain tunable polarization
in the VUV and X-ray spectral range. Experimental results are successfully
compared to those obtained using a theoretical model based on the paraxial
solution of Maxwell's equations. Our findings can be expected to have a deep
impact on the design and realization of experiments requiring full control of
light polarization to explore the symmetry properties of matter samples