Reconstructing a 3D structure from a set of its 2D X-ray projections requires that the source position and image plane orientation in 3D space be obtained with high accuracy for each of the imaging chain positions. This knowledge is generally obtained through a geometrical calibration of the data acquisition system. In this paper, we present a fully automatic method for such a geometrical calibration, well suited to a 3D X-ray imaging system which acquires sets of 2D projections during a rotation of the imaging chain. This method is based on (1) the use of a dedicated calibration phantom with reference points, (2) an automatic algorithm to detect and identify the reference points on the phantom's 2D X-Ray projections, and (3) the estimation of the imaging chain geometrical parameters by minimizing the reprojection mean quadratic error measured on these reference points. Results obtained both from simulation data and from data acquired on an experimental bench are presented.