High precision astrometry requires an accurate geometric distortion solution. In this work, we present an average correction for the Blue Camera of the Large Binocular Telescope which enables a relative astrometric precision of ~15 mas for the B_Bessel and V_Bessel broad-band filters. The result of this effort is used in two companion papers: the first to measure the absolute proper motion of the open cluster M67 with respect to the background galaxies; the second to decontaminate the color-magnitude diagram of M67 from field objects, enabling the study of the end of its white dwarf cooling sequence. Many other applications might find this distortion correction useful.