  Self interacting dark matter (SIDM) provides us with a consistent solution to
certain astrophysical observations in conflict with collision-less cold DM
paradigm. In this work we estimate the shear viscosity $(\eta)$ and bulk
viscosity $(\zeta)$ of SIDM, within kinetic theory formalism, for galactic and
cluster size SIDM halos. To that extent we make use of the recent constraints
on SIDM crossections for the dwarf galaxies, LSB galaxies and clusters. We also
estimate the change in solution of Einstein's equation due to these viscous
effects and find that $\sigma/m$ constraints on SIDM from astrophysical data
provide us with sufficient viscosity to account for the observed cosmic
acceleration at present epoch, without the need of any additional dark energy
component. Using the estimates of dark matter density for galactic and cluster
size halo we find that the mean free path of dark matter $\sim$ few Mpc. Thus
the smallest scale at which the viscous effect start playing the role is
cluster scale. Astrophysical data for dwarf, LSB galaxies and clusters also
seems to suggest the same. The entire analysis is independent of any specific
particle physics motivated model for SIDM.
