The invention relates to a method for contactless recording of a track geometry of a track by means of a rail vehicle which is moved along the track on on-track undercarriages (4), wherein profile data of the track extending in transverse direction are compiled by means of a laser scanner. In this, it is provided that, by means of an evaluation device, profile data are evaluated relative to a reference base pre-defined on the rail vehicle in order to derive from this the course of a track central axis and/or a rail. The invention additionally relates to a rail vehicle which comprise an evaluation device configured for carrying out the method. Thus, no further measuring system is required to determine a track position.