A method is presented to estimate the acquisition geometry of a pinhole single photon emission computed tomography (SPECT) camera with a circular detector orbit. This information is needed for the reconstruction of tomographic images. The calibration uses the point source projection locations of a tomographic acquisition of three point sources located at known distances from each other. It is shown that this simple phantom provides the necessary and sufficient information for the proposed calibration method. The knowledge of two of the distances between the point sources proves to be essential. The geometry is estimated by fitting analytically calculated projections to the measured ones, using a simple least squares Powell algorithm. Some mild a priori knowledge is used to constrain the solutions of the fit. Several of the geometrical parameters are however highly correlated. The effect of these correlations on the reconstructed images is evaluated in simulation studies and related to the estimation accuracy. The highly correlated detector tilt and electrical shift are shown to be the critical parameters for accurate image reconstruction. The performance of the algorithm is finally demonstrated by phantom measurements. The method is based on a single SPECT scan of a simple calibration phantom, executed immediately after the actual SPECT acquisition. The method is also applicable to cone-beam SPECT and X-ray CT.