  Pulsars are magnetized rotating compact objects. They spin down due to
magnetic dipole radiation and wind emission. If photon has a nonzero mass, the
spin down rate would be smaller than the zero mass case. We show that an upper
limit of the photon mass, i.e. $m_\gamma\lesssim h/Pc^2$, may be placed if a
pulsar with period $P$ is observed to spin down. Recently, a white dwarf (WD)
--- M dwarf binary, AR Scorpii was discovered to emit pulsed broadband emission
with pulses. The spin-down luminosity of the WD can comfortably power the
non-thermal radiation from the system. Applying our results to the WD pulsar
with $P=117~\rm{s}$, we obtain a stringent upper limit of the photon mass
between $m_\gamma<6.3\times10^{-50}~\rm{g}$ assuming a vacuum dipole spindown,
and $m_\gamma<9.6\times10^{-50}~\rm{g}$ assuming a spindown due to a fully
developed pulsar wind.
