  The weak field approximation in a model of de Sitter gravity is investigated
in the static and spherically symmetric case, under the assumption that the
vacuum spacetime without perturbations from matter fields is a torsion-free de
Sitter spacetime. It is shown on one hand that any solution should be singular
at the center of the matter field, if the exterior is described by a
Schwarzschild-de Sitter spacetime and is smoothly connected to the interior. On
the other, all the regular solutions are obtained, which might be used to
explain the galactic rotation curves without involving dark matter.
