  The Deser-Woodard (DW) nonlocal gravity model has been proposed in order to
describe the late-time acceleration of the universe without introducing dark
energy. In this paper we focus, however, on the early stage of the universe and
demonstrate how a primordial bounce in the vacuum spacetime can be realized in
the framework of the DW nonlocal model. We reconstruct the nonlocal distortion
function, which encodes all the modifications to the Einstein-Hilbert action,
in order to generate bouncing solutions to solve the initial singularity
problem. We show that the initial conditions can be chosen in such a way that
the distortion function and its first order derivative approach zero after the
bounce and the standard cosmological solution described by general relativity
is recovered afterwards. We also study the evolution of anisotropies near the
bounce. It turns out that the shear density defined by the anisotropy grows
towards the bounce, but due to the presence of nonlocal effects, it grows in a
milder manner compared with that in Einstein gravity.
