ALFA is part of the ATLAS Roman Pot detector dedicated to measure protons scattered at very small angles in proton-proton collisions at the LHC. ALFA aims to study elastic and diffractive events in special runs with reduced luminosity and optimized beam optics. Precision of the measurement depends on the correct positioning of the ALFA detector with respect to the actual beam position. For this purpose a track-based procedure is used which utilizes tracks of beam halo and elastic protons collected during physics data taking. This paper presents results of fast and robust alignment of ALFA detectors during LHC Run 2. The alignment constants are used in analysis of diffractive events and also serve as preliminary values in elastic event analysis. Precise measurements of the elastic cross sections require more precise dedicated alignment.