  We introduce a scheme to entangle Rydberg ions in a linear ion crystal, using
the high electric polarizability of the Rydberg electronic states in
combination with mutual Coulomb coupling of ions that establishes common modes
of motion. After laser-initialization of ions to a superposition of ground- and
Rydberg-state, the entanglement operation is driven purely by applying a
voltage pulse that shuttles the ion crystal back and forth. This operation can
achieve entanglement on a sub-$\mu$s timescale, more than two orders of
magnitude faster than typical gate operations driven by continuous-wave lasers.
Our analysis shows that the fidelity achieved with this protocol can exceed
$99.9\%$ with experimentally achievable parameters.
