RESUMEN
The beam energy of the circular electron-positron collider should be measured precisely to the order of 1 MeV, in order to decrease the uncertainty of the Higgs/W/Z bosons' mass measurement. For this purpose, a lepton bunch is extracted from the collider and collides with an Yttrium-Aluminum-Garnet laser pulse. After the inverse Compton scattering, the main beam and the scattered beam pass through an analytical magnetic field and are deflected to different angles. At the end of the drift beam pipes, the deflecting distances are detected with the spatial resolution of several microns. The systematic uncertainties caused by the detector arrangement, the magnetic field, the angle between the detector plane and the incident beam, and the synchrotron radiation are discussed in detail. The simulations of the statistical errors are given with a toy Monte Carlo sample. With some proper corrections, the beam energy uncertainty of the Higgs mode is around 2 MeV. Our method is applicable to different operating modes of the collider.