  We demonstrate excitation of a single trapped cold $^{40}$Ca$^+$ ion to
Rydberg levels by laser radiation in the vacuum-ultraviolet at 122 nm
wavelength. Observed resonances are identified as 3d$^2$D$_{3/2}$ to 51 F, 52 F
and 3d$^2$D$_{5/2}$ to 64F. We model the lineshape and our results imply a
large state-dependent coupling to the trapping potential. Rydberg ions are of
great interest for future applications in quantum computing and simulation, in
which large dipolar interactions are combined with the superb experimental
control offered by Paul traps.
