The Voyager 1 spacecraft had a close encounter (miss distance = 6870 km) with Titan (diameter = 5140 km) on November 12, 1980, while this large satellite was located within the Saturian magnetosphere at a local solar time of 1330. No clear evidence was found for any intrinsic magnetic field nor for the development of a bow shock wave as the corotating Saturnian magnetoplasma convected past Titan. However, a strong electrodynamic interaction was evidenced with the observation of a very developed, induced bipolar magnetic tail. Three thin current carrying regions were crossed, corresponding to the inbound and outbound tail magnetopause and an imbedded tail neutral sheet. An asymmetry in the tail axis orientation of 20 with respect to the corotation direction was observed. Also seen was an asymmetry in the structure of the two tail lobes. This interaction is unique among those in the solar system observed to date, being intermediate in the characteristic Mach numbers, both sonic and Alfvenic, when compared with Titan (or Venus) in the solar wind or Io in the Jovian magnetosphere. This paper presents the results of the analysis of the magnetic field data, which suggest an interpretation qualitatively described by the draping of the Saturnian magnetic field around the ionosphere of Titan.