Aims.We have performed optical polarimetric observations of the SN 2006aj associated to the X-ray flash (XRF) of February 18, 2006, XRF 060218 that provide information on its expansion geometry. Methods: .The data were acquired in the R-band with the 0.7 m telescope of Crimea, 2.5 m Nordic Optical Telescope and the 2.2 m of Calar Alto. Results: .We report the detection of linear polarization between 3 and 39 days after the gamma-ray event (t-t_0). This represents the first polarization detection of a Ic supernova (SN) associated to an XRF. Our data exhibit a degree of linear polarization (P) around P˜4% at t-t0 ˜ 3{-}5 days, followed by a constant polarization phase with P ˜ 1.4% at 13.7 ⪉ t-t0 ⪉ 39 days. Our data suggest a decay in P, and more interestingly, show a position angle (θ) rotation of 100° comparing data taken before and after the R-band lightcurve peak. Conclusions: .The reported polarization measurements can be explained by the evolution of an asymmetric SN expansion. We discuss on several ingredients that could account for the observed θ rotation.