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 overdensity along the direction of motion. To test this hypothesis, we fit (and subtract) symmetric haloes to the weak gravitational data of 72 merging galaxy clusters observed with the Hubble Space Telescope. We convert the shear directly into excess. 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 M-gas/M-dm = 0.13 +/- 0.035. We find no evidence for scattered dark matter particles with an 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 arcsec, then we will be able to detect a scattering fraction of 10 per cent at the 3 sigma level with current surveys. This potentially interesting new method can provide an important independent test for other complimentary studies of the self-interaction cross-section of dark matter.