  We have measured the AC-Stark shift of the $14D_{5/2}$ Rydberg state of
rubidium 87 in an optical dipole trap formed by a focussed CO$_2$-laser. We
find good quantitative agreement with the model of a free electron experiencing
a ponderomotive potential in the light field. In order to reproduce the
observed spectra we take into account the broadening of the Rydberg state due
to photoionization. The extracted cross-section is compatible with previous
measurements on neighboring Rydberg states.
