  Dark matter (DM) can consist of very light bosons behaving as a classical
scalar field that experiences coherent oscillations. The presence of this DM
field would perturb the dynamics of celestial bodies, either because the
(oscillating) DM stress tensor modifies the gravitational potentials of the
galaxy, or if DM is directly coupled to the constituents of the body. We study
secular variations of the orbital parameters of binary systems induced by such
perturbations. Two classes of effects are identified. Effects of the first
class appear if the frequency of DM oscillations is in resonance with the
orbital motion; these exist for general DM couplings including the case of
purely gravitational interaction. Effects of the second class arise if DM is
coupled quadratically to the masses of the binary system members and do not
require any resonant condition. The exquisite precision of binary pulsar timing
can be used to constrain these effects. Current observations are not sensitive
to oscillations in the galactic gravitational field, though a discovery of
pulsars in regions of high DM density may improve the situation. For DM with
direct coupling to ordinary matter, the current timing data are already
competitive with other existing constraints in the range of DM masses $\sim
10^{-22}-10^{-18}\,{\rm eV}$. Future observations are expected to increase the
sensitivity and probe new regions of parameters.
