Binary neutron star mergers are considered to be the most favorable sources that produce electromagnetic (EM) signals associated with gravitational waves (GWs). They are also the likely progenitors of short duration gamma-ray bursts (GRBs). The brief gamma-ray emission (the “prompt” GRB emission) is produced by ultra-relativistic jets, as a result, it is strongly beamed over a small solid angle along the jet. As a result is estimated to be a decade or so before a short GRB jet within the LIGO volume points along our line of sight. However, we argue that for a realistic jet model, one whose luminosity and Lorentz factor vary smoothly with angle, the prompt signal can be detected for a significantly broader range of viewing angles. This can lead to an “off-axis” short GRB as an EM counterpart. Our estimates and simulations show, that with the aid of the temporal coincidence from a LIGO trigger, it is feasible to detect these prompt signals with a detector such as Fermi, even if the observer is substantially misaligned with respect to the jet.