The inherent small divergence angle of space optical communication poses significant challenges to establishing communication links. Therefore, laser link acquisition becomes a crucial technology in optical communication, with a primary focus on reducing the acquisition time effectively. Conventional optical communication acquisition techniques fail to address the error effects caused by satellite insertion into the Earth orbit, thus unable to meet the rapid establishment demands of laser links in satellite optical communication networks. In this regard, we propose a novel, to the best of our knowledge, on-orbit calibration method for laser communication terminals to our knowledge. Leveraging stellar observations, this method achieves efficient on-orbit calibration with only a single observation. Theoretical analysis and on-orbit experimental results demonstrate that this approach effectively enhances an open-loop pointing accuracy, offering promising prospects for achieving a rapid establishment of optical communication links in ultra-long-distance optical communication missions.