This paper proposes a scan method to reduce the acquisition time of inter-satellite links based on the satellite position error distribution. The errors are modeled as an anisotropic multivariate Gaussian distribution, and the field of uncertainty (FOU) is defined as the 5-sigma region of this distribution. Due to the significant errors typically found in the along-track direction, the FOU often takes an elliptical shape. We propose a scanning pattern to scan the elliptical FOU efficiently. Our approach was validated through Monte-Carlo simulations and analyses using GPS data from NEXTSat-2. The results indicate that the proposed scan method is more effective than the traditional method when the FOU is more elliptical. In the case of NEXTSat-2, the efficiency of the proposed method was confirmed, with the ratio of the semi-minor to the semi-major axis was less than 0.2 in 70% of cases.