Aims. We study possible signs of asymmetry in the luminous type IIn SN 2010jl, to obtain independent information about its explosion geometry. Methods. We performed optical linear spectropolarimetry of SN 2010jl two weeks after the discovery, in the spectral range 3700-8800 Å.Results. The object exhibits a continuum polarization at a very significant and almost constant level (1.7-2.0%). Distinctive line depolarization is seen at the positions of the strongest emission features, such as Hα and Hβ. This implies that the line forming region is well above the photosphere. The continuum polarization level (1.7-2.0%) indicates a substantial asphericity, of axial ratio ≤0.7. The almost complete depolarization seen at Hα is indicative of a very low level of interstellar polarization (≤0.3%). This rules out the presence of relevant amounts of dust in the progenitor environment at the time of our observations. From a polarimetric point of view, SN 2010jl appears to be very similar to the two other well-studied type IIn SNe 1997eg and 1998S, establishing a strong link between members of this class of objects.