The subaperture stitching interferometry is a technique suitable for testing high numerical-aperture optics, large-diameter spherical lenses and aspheric optics. In the stitching process, each subaperture has to be placed at its correct position in a global coordinate, and the positioning precision would affect the accuracy of stitching result. However, the mechanical limitations in the alignment process as well as vibrations during the measurement would induce inevitable subaperture position uncertainties. In our previous study, a rotational scanning subaperture stitching interferometer has been constructed. This paper provides an iterative algorithm to correct the subaperture position without altering the interferometer configuration. Each subaperture is first placed at its geometric position estimated according to the F number of reference lens, the measurement zenithal angle and the number of pixels along the width of subaperture. By using the concept of differentiation, a shift compensator along the radial direction of the global coordinate is added into the stitching algorithm. The algorithm includes two kinds of compensators: one for the geometric null with four compensators of piston, two directional tilts and defocus, and the other for the position correction with the shift compensator. These compensators are computed iteratively to minimize the phase differences in the overlapped regions of subapertures in a least-squares sense. The simulation results demonstrate that the proposed method works to the position accuracy of 0.001 pixels for both the single-ring and multiple-ring configurations. Experimental verifications with the single-ring and multiple-ring data also show the effectiveness of the algorithm.