In this work, we propose to use a pinhole camera at high photon energies, specifically 200-300 keV, to measure ultra-small electron beam size by means of bending magnet radiation. We show that there is a sufficient photon flux at the detector position. Our theoretical analysis includes an examination of the applicability of the van Cittert-Zernike theorem for the bending magnet radiation generated by an ultralow emittance electron beam and a detailed analysis of the imaging properties of rectangular pinhole cameras. This led us to practical, universal formulas. We identify the optimal aperture size and resolution of the camera in the given geometry. The theoretical findings are further substantiated by wavefront propagation numerical simulations of partially coherent radiation. This study serves both as a practical guide for optical engineering and an educational resource for explaining the imaging properties of pinhole cameras.