  As binary systems move inside galaxies, they interact with the dark matter
halo. This interaction leads to the accretion of dark matter particles inside
binary components. The accretion of dark matter particles increases the mass of
the binary components and then, the total mass of the system. Increased mass by
this way can affect other physical parameters of the systems, like orbital
periods of the systems. In this work, we estimated the period change of some
known compact binary systems due to the accretion of dark matter particles
inside them. Our conclustion is that, for WIMP particles with masses in the
range $\simeq 10 \: GeV.c^{-2}$ and dark matter density as high as the dark
matter density around the sun, period change due to accretion of dark matter
partices is negligible compared to the period change due to the emission of
gravitaional waves from the systems.
