When an intense laser field interacts with molecules, a variety of characteristic dynamics come into play such as ionization, dissociation, fragmentation, and isomerization. Here we experimentally investigate the effect of laser intensity and polarization of ultrashort laser pulses on dissociative double ionization of acetylene, in particular on the ultrafast proton migration. A significant increase of the relative yield of the proton migration channel versus the symmetric break-up channel with increase in intensity and the change of polarization from linear to circular is observed.