  An implementation of A Common Tracking Software (ACTS) toolkit for signal
electron reconstruction for the COMET muon to electron conversion experiment is
discussed. The COMET experiment in J-PARC, Japan, will search for neutrinoless
conversion of muons into electrons in the field of an aluminium nucleus, a
lepton flavour violating process, aiming target sensitivity of $10^{-17}$. To
achieve its scientific goals, the experiment requires a reconstructed momentum
resolution of lower than 150 keV/c. For the first time by applying ACTS to
signal events in the 100 MeV energy range with multiple-turn trajectories in
the presence of background events, it is found that the reconstruction
efficiency is around 14\% with no fake reconstructed events. The implementation
details, performance, and issues of ACTS in the context of COMET are presented.
