The electromagnetic radiation by quark-gluon plasma in a strong magnetic field is calculated. The contributing processes are synchrotron radiation and one-photon annihilation. It is shown that in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) synchrotron radiation dominates over the annihilation. Moreover, it constitutes a significant part of all photons produced by the plasma at low transverse momenta; its magnitude depends on the plasma temperature and the magnetic field strength. Electromagnetic radiation in a magnetic field is probably the missing piece that resolves a discrepancy between the theoretical models and the experimental data. It is argued that electromagnetic radiation increases with the magnetic field strength and plasma temperature.