All computed-tomography (CT) reconstruction algorithms used today require knowledge of the central ray, which is the projection of the center of rotation (COR) on the detector. The current common practice is to determine it using a wire phantom made of a dense metal material before the CT scan of the object to be inspected. This work presents four methods that can be used for this purpose, the center-of-sinogram, the opposite-angle-interpolation, curve-fitting, and geometrical methods. To our best knowledge, the last two approaches have not been reported before. The performance of the four methods is evaluated under four different situations. The comparison study shows that for all situations, the curve-fitting method and the interpolation method have consistent performance, and that only when the wire-to-COR is small, can all four methods generate close results. When the wire-to-COR distance becomes large, the center-of-sinogram method is generally not reliable. Although in principle the geometrical method is able to provide an exact solution, in practice its accuracy is limited by the finite size of the detector pixel and can be improved if the detector pixel size becomes smaller.