  Context. The 98{\deg}-obliquity of Uranus is commonly attributed to giant
impacts that occurred at the end of the planetary formation. This picture,
however, is not devoid of weaknesses.
  Aims. On a billion-year timescale, the tidal migration of the satellites of
Jupiter and Saturn has been shown to strongly affect their spin-axis dynamics.
We aim to revisit the scenario of tilting Uranus in light of this mechanism.
  Methods. We analyse the precession spectrum of Uranus and identify the
candidate secular spin-orbit resonances that could be responsible for the
tilting. We determine the properties of the hypothetical ancient satellite
required for a capture and explore the dynamics numerically.
  Results. If it migrates over 10 Uranus' radii, a single satellite with
minimum mass 4e-4 Uranus' mass is able to tilt Uranus from a small obliquity
and make it converge towards 90{\deg}. In order to achieve the tilting in less
than the age of the Solar System, the mean drift rate of the satellite must be
comparable to the Moon's current orbital expansion. Under these conditions,
simulations show that Uranus is readily tilted over 80{\deg}. Beyond this
point, the satellite is strongly destabilised and triggers a phase of chaotic
motion for the planet's spin axis. The chaotic phase ends when the satellite
collides into the planet, ultimately freezing the planet's obliquity in either
a prograde, or plainly retrograde state (as Uranus today). Spin states
resembling that of Uranus can be obtained with probabilities as large as 80%,
but a bigger satellite is favoured, with mass 1.7e-3 Uranus' mass or more. Yet,
a smaller ancient satellite is not categorically ruled out, and there is room
for improving this basic scenario in future studies. Interactions among several
pre-existing satellites is a promising possibility.
