We present a new coalignment method for the EUV Imaging Spectrometer (EIS) on board the Hinode spacecraft. In addition to the pointing offset and spacecraft jitter, this method determines the roll angle of the instrument, which has never been systematically measured, and which is therefore usually not corrected. The optimal pointing for EIS is computed by maximizing the cross-correlations of the Fe xii 195.119 Å line with images from the 193 Å band of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). By coaligning 3336 rasters with high signal-to-noise ratio, we estimate the rotation angle between EIS and AIA and explore the distribution of its values. We report an average value of (-0.387 ± 0.007)°. We also provide a software implementation of this method that can be used to coalign any EIS raster.