A synchrotron X-ray microscope is a powerful imaging apparatus for taking high-resolution and high-contrast X-ray images of nanoscale objects. A sufficient number of X-ray projection images from different angles is required for constructing 3D volume images of an object. Because a synchrotron light source is immobile, a rotational object holder is required for tomography. At a resolution of 10 nm per pixel, the vibration of the holder caused by rotating the object cannot be disregarded if tomographic images are to be reconstructed accurately. This paper presents a computer method to compensate for the vibration of the rotational holder by aligning neighboring X-ray images. This alignment process involves two steps. The first step is to match the "projected feature points" in the sequence of images. The matched projected feature points in the x-θ plane should form a set of sine-shaped loci. The second step is to fit the loci to a set of sine waves to compute the parameters required for alignment. The experimental results show that the proposed method outperforms two previously proposed methods, Xradia and SPIDER. The developed software system can be downloaded from the URL, http://www.cs.nctu.edu.tw/~chengchc/SCTA or http://goo.gl/s4AMx.