Singular points are critical features of fingerprints. They are broadly used in fingerprint registration and many other applications. The rotation estimation of singular points can largely affect the performance of a fingerprint registration method. Most existing algorithms detect singular points directly from the available ridge orientation structures. However, the performance degrades if the singular patterns in a fingerprint image are incomplete. In this paper, we propose a model-based method for estimating the angular difference between singular points. The proposed method exploits analytical features derived from ridge orientation models and is more robust with incomplete fingerprints. We test the proposed method with manually rotated fingerprints generated from the FVC2002 DB1a database. The performance is evaluated by mean square errors (MSE) and ROC curves.