  We investigate the charmed baryon mass spectrum using the relativistic heavy
quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3
\times 64$ lattice. The dynamical up-down and strange quark masses are tuned to
their physical values, reweighted from those employed in the configuration
generation. At the physical point, the inverse lattice spacing determined from
the $\Omega$ baryon mass gives $a^{-1}=2.194(10)$ GeV, and thus the spatial
extent becomes $L = 32 a = 2.88(1)$ fm. Our results for the charmed baryon
masses are consistent with experimental values, except for the mass of
$\Xi_{cc}$, which has been measured by only one experimental group so far and
has not been confirmed yet by others. In addition, we report values of other
doubly and triply charmed baryon masses, which have never been measured
experimentally.
