For over a decade, it has been debated whether the concordance LCDM model is consistent with the observed abundance of giant arcs in clusters. While previous theoretical studies have focused on properties of the lens and source populations, as well as cosmological effects such as dark energy, the impact of initial conditions on the giant-arc abundance is relatively unexplored. Here, we quantify the impact of non-Gaussian initial conditions with the local bispectrum shape on the predicted frequency of giant arcs. Using a path-integral formulation of the excursion set formalism, we extend a semi-analytic model for calculating halo concentrations to the case of primordial non-Gaussianity, which may be useful for applications outside of this work. We find that massive halos tend to collapse earlier in models with positive f_NL, relative to the Gaussian case, leading to enhanced concentration parameters. The converse is true for f_NL < 0. In addition to these effects, which change the lensing cross sections, non-Gaussianity also modifies the abundance of supercritical clusters available for lensing. These combined effects work together to either enhance (f_NL > 0) or suppress (f_NL < 0) the probability of giant-arc formation. Using the best value and 95% confidence levels currently available from the Wilkinson Microwave Anisotropy Probe, we find that the giant-arc optical depth for sources at z_s~2 is enhanced by ~20% and ~45% for f_NL = 32 and 74 respectively. In contrast, we calculate a suppression of ~5% for f_NL = -10. These differences translate to similar relative changes in the predicted all-sky number of giant arcs.
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