The Alpha Magnetic Spectrometer (AMS) is a high energy physics experiment operating aboard the International Space Station (ISS) since May 2011. So far more than 100 billion of charged cosmic ray events have been collected by AMS. The AMS silicon tracker, together with the magnet, measures the rigidity (momentum/charge) of cosmic rays in the range from 0.5 GV to several TV. To accurately determine the trajectory of charged particles, a novel tracker position reconstruction method has been developed. In the paper, the details of the method and the obtained tracker spatial resolution for nuclei with charge from 2 to 26 are presented.