One of the main features of Weyl semimetals is the existence of Fermi arc surface states at their surface, which cannot be realized in pure two-dimensional systems in the absence of many-body interactions. Due to the gapless bulk of the semimetal, it is, however, challenging to observe clear signatures from the Fermi arc surface states. Here, we propose to detect such novel surface states via perfect negative refraction that occurs between two adjacent open surfaces with properly orientated Fermi arcs. Specifically, this phenomenon visibly manifests in nonlocal transport measurement, where the negative refraction generates a return peak in the realspace conductance. This provides a unique signature of the Fermi arc surface states. We discuss the appearance of this peak in both inversion- and time-reversal-symmetric Weyl semimetals, where the latter exhibits conductance oscillations due to multiple negative refraction scattering events.