ArgoNeuT, or Argon Neutrino Test, is a 170 liter liquid argon time projection chamber designed to collect neutrino interactions from the NuMI beam at Fermi National Accelerator Laboratory. ArgoNeuT operated in the NuMI low-energy beam line directly upstream of the MINOS Near Detector from September 2009 to February 2010, during which thousands of neutrino and antineutrino events were collected. The MINOS Near Detector was used to measure muons downstream of ArgoNeuT. Though ArgoNeuT is primarily an R&D project, the data collected provide a unique opportunity to measure neutrino cross sections in the 0.1-10 GeV energy range. Fully reconstructing the muon from these interactions is imperative for these measurements. This paper focuses on the complete kinematic reconstruction of neutrino-induced through-going muons tracks. Analysis of this high statistics sample of minimum ionizing tracks demonstrates the reliability of the geometric and calorimetric reconstruction in the ArgoNeuT detector.