We present the results from a weak gravitational lensing study of the merging cluster A520 based on the analysis of Hubble Space Telescope/Advanced Camera for Surveys (ACS) data. The excellent data quality allows us to reach a mean number density of source galaxies of ~109 per sq. arcmin, which improves both resolution and significance of the mass reconstruction compared to a previous study based on Wide Field Planetary Camera 2 (WFPC2) images. We take care in removing instrumental effects such as the trailing of charge due to radiation damage of the ACS detector and the position-dependent point spread function (PSF). This new ACS analysis confirms the previous claims that a substantial amount of dark mass is present between two luminous subclusters. We examine the distribution of cluster galaxies and observe very little light at this location. We find that the centroid of the dark peak in the current ACS analysis is offset to the southwest by ~1 arcmin with respect to the centroid from the WFPC2 analysis. Interestingly, this new centroid is in better spatial agreement with the location where the X-ray emission is strongest, and the mass-to-light ratio estimated with this centroid is much higher 813+-78 M_sun/L_Rsun than the previous value; the aperture mass based on the WFPC2 centroid provides a slightly lower, but consistent mass. Although we cannot provide a definite explanation for the presence of the dark peak, we discuss a revised scenario, wherein dark matter with a more conventional range sigma_DM/m_DM < 1 cm^2/g of self-interacting cross-section can lead to the detection of this dark substructure. If supported by detailed numerical simulations, this hypothesis opens up the possibility that the A520 system can be used to establish a lower limit of the self-interacting cross-section of dark matter.