We have measured the sticking coefficient of H-2 on Pd(lll) as a function of incident translational energy, over the range 31-94 meV, and initial H-2 rotational state J, for J=0 through J=5, at a surface temperature of 423 K. These measurements test recent theoretical predictions that the H-2/Pd sticking coefficient should decrease with increasing J, for low J, because more quickly rotating molecules are less easily "steered" to dissociation sites by interaction with the surface as they approach the metal [A. Gross, S. Wilke, and M. Scheffler, Phys. Rev. Lett. 75, 2718 (1995)]. We find that the sticking coefficient is sensitive to the rotational quantum number, first decreasing as J is raised from 0 to 3, then increasing again for J=4 and 5. The greatest sensitivity found occurs for an incident translational energy of 73 meV, for which the sticking coefficient decreases from 0.76+/-0.05 for J=0 to 0.54+/-0.13 for J=3. In addition, we have found that a fraction of the H-2 incident in states J=0 and J=1 is excited to states J=2 and J=3, respectively, upon collision with the surface, with a probability that increases strongly with surface temperature and is roughly independent of incident translational energy. This rotational excitation does not result from dissociation followed by recombinative desorption, but occurs directly upon scattering from the surface. Furthermore, the majority of tile excitation energy comes from the surface, and not from the incident translational energy of the molecule. The J-dependent sticking coefficients and the rotational excitation of the incident molecule by the surface are together strong evidence for a coupling between the surface and the rotational degree of freedom of the incident molecule, and support the model of dynamical steering in the adsorption process.