  Context. As a star evolves, the planet orbits change with time due to tidal
interactions, stellar mass losses, friction and gravitational drag forces, mass
accretion and evaporation on/by the planet. Stellar rotation modifies the
structure of the star and therefore the way these different processes occur.
Changes of the orbits, at their turn, have an impact on the rotation of the
star.
  Aims. Models accounting in a consistent way for these interactions between
the orbital evolution of the planet and the evolution of the rotation of the
star are still missing. The present work is a first attempt to fill this gap.
  Methods. We compute the evolution of stellar models including a comprehensive
treatment of rotational effects together with the evolution of planetary
orbits, so that the exchanges of angular momentum between the star and the
planetary orbit are treated in a self-consistent way. The evolution of the
rotation of the star accounts for the angular momentum exchange with the planet
and also follows the effects of the internal transport of angular momentum and
chemicals.
  Results. We show that rotating stellar models without tidal interactions can
well reproduce the surface rotations of the bulk of the red giants. However,
models without any interactions cannot account for fast rotating red giants in
the upper part of the red giant branch, where, such models, whatever the
initial rotation considered on the ZAMS, always predict very low velocities.
For those stars some interaction with a companion is highly probable and the
present rotating stellar models with planets confirm that tidal interaction can
reproduce their high surface velocities. We show also that the minimum distance
between the planet and the star on the ZAMS that will allow the planet to avoid
engulfment and survive is decreased around faster rotating stars. [abridged]
