The terahertz photoconductivity in epitaxial graphene grown on SiC substrates is investigated in a magnetic field. The magnetic-field dependence of the photoresponse signal amplitude is examined at different electron densities, bias currents, and terahertz radiation intensities. The experimental results are explained well by a photoconductivity mechanism based on the heating of electrons by terahertz radiation. A strong increase in the photoconductivity signal with increasing magnetic field caused by an increase in the relaxation time due to the suppression of electron-electron scattering is observed.