  The obliquity of a planet is the tilt between its equator and its orbital
plane. Giant planets are expected to form with near-zero obliquities. After its
formation, some dynamical mechanism must therefore have tilted Saturn up to its
current obliquity of 26.7{\deg}. This event is traditionally thought to have
happened more than 4 Gyrs ago during the late planetary migration because of
the crossing of a resonance between the spin-axis precession of Saturn and the
nodal orbital precession mode of Neptune. Here, we show that the fast tidal
migration of Titan measured by Lainey et al. (2020) is incompatible with this
scenario, and that it offers a new explanation for Saturn's current obliquity.
A significant migration of Titan would prevent any early resonance,
invalidating previous constraints on the late planetary migration set by the
tilting of Saturn. We propose instead that the resonance was encountered
recently, about 1 Gyr ago, forcing Saturn's obliquity to increase from a small
value (possibly less than 3{\deg}), up to its current state. This scenario
suggests that Saturn's normalised polar moment of inertia lies between 0.224
and 0.237. Our findings bring out a new paradigm for the spin-axis evolution of
Saturn, Jupiter, and possibly giant exoplanets in multiple systems, whereby
obliquities are not settled once for all, but continuously evolve as a result
of the migration of their satellites.
