  Using radiative Z^0 -> \tau^+ \tau^- \gamma events collected with the OPAL
detector at LEP at \sqrt{s}= M_Z during 1990-95, a direct study of the
electromagnetic current at the \tau\gamma vertex has been performed in terms of
the anomalous magnetic form factor F_2 of the \tau lepton. The analysis is
based on a data sample of 1429 e^+ e^- -> \tau^+ \tau^- \gamma events which are
examined for a deviation from the expectation with F_2 = 0. From the
non-observation of anomalous \tau^+ \tau^- \gamma production a limit of
  -0.068 < F_2 < 0.065
  is obtained. This can also be interpreted as a limit on the electric dipole
form factor F_3 as
  -3.8 x 10^-16 e-cm < eF_3 < 3.6 x 10^-16 e-cm.
  The above ranges are valid at the 95% confidence level.
