The Joule-Thomson coefficient μ(P, T) is computed from the virial equation of state up to seventh-order for argon obtained from accurate ab initio data. Higher-order corrections become increasingly more important to fit the low-temperature and low-pressure regime and to avoid the early onset of divergence in the Joule-Thomson inversion curve. Good agreement with experiment is obtained for temperatures T > 250 K. The results also illustrate the limitations of the virial equation in regions close to the critical temperature.