  If dark matter interacts, even weakly, via non-gravitational forces,
simulations predict that it will be preferentially scattered towards the
trailing edge of the halo during collisions between galaxy clusters. This will
temporarily create a non-symmetric mass profile, with a trailing over-density
along the direction of motion. To test this hypothesis, we fit (and subtract)
symmetric halos to the weak gravitational data of 72 merging galaxy clusters
observed with the Hubble Space Telescope. We convert the shear directly into
excess {\kappa} and project in to a one dimensional profile. We generate
numerical simulations and find that the one dimensional profile is well
described with simple Gaussian approximations. We detect the weak lensing
signal of trailing gas at a 4{\sigma} confidence, finding a mean gas fraction
of Mgas/Mdm = 0.13 +/- 0.035. We find no evidence for scattered dark matter
particles with a estimated scattering fraction of f = 0.03 +/- 0.05. Finally we
find that if we can reduce the statistical error on the positional estimate of
a single dark matter halo to <2.5", then we will be able to detect a scattering
fraction of 10% at the 3{\sigma} level with current surveys. This poten- tially
interesting new method can provide an important independent test for other
complimentary studies of the self-interaction cross-section of dark matter.
