  We consider weakly magnetized hot QED plasma comprising electrons and
positrons. There are three distinct dispersive (longitudinal and two
transverse) modes of a photon in a thermo-magnetic medium. At lowest order in
coupling constant, photon is damped in this medium via Compton scattering and
pair creation process. We evaluate the damping rate of hard photon by
calculating the imaginary part of the each transverse dispersive modes in a
thermo-magnetic QED medium. We note that one of the fermions in the loop of
one-loop photon self-energy is considered as soft and the other one is hard.
Considering the resummed fermion propagator in a weakly magnetized medium for
the soft fermion and the Schwinger propagator for hard fermion, we calculate
the soft contribution to the damping rate of hard photon. In weak field
approximation the thermal and thermo-magnetic contributions to damping rate get
separated out for each transverse dispersive mode. The total damping rate for
each dispersive mode in presence of magnetic field is found to be reduced than
that of the thermal one. This formalism can easily be extended to QCD plasma.
