We have studied the adsorption of a weak flexible polyelectrolyte, poly(acrylic acid), at an oppositely charged surface, the surface of water covered with a Langmuir film of dimethyldioctadecylammonium bromide. The surface charge density and the polymer ionization degree a were conveniently varied by varying respectively the density a of the Langmuir film and the pH of the polyelectrolyte solution. By infrared spectroscopy we evidenced a change in the mean orientation of the adsorbed chains when increasing the surface charge density, from parallel to the surface for sigma(0) < sigma(0) to perpendicular to the surface for sigma(0) > sigma(0). A signature of this regime change also appears in the compression elastic modulus. The value of sigma(0) scales as alpha at low alpha, as predicted by theory, but saturates when increasing alpha, presumably because of a saturation of the polyelectrolyte charge fraction.