  We present a protocol for using trapped ions to measure rotations via
matter-wave Sagnac interferometry. The trap allows the interferometer to
enclose a large area in a compact apparatus through repeated round-trips in a
Sagnac geometry. We show how a uniform magnetic field can be used to close the
interferometer over a large dynamic range in rotation speed and measurement
bandwidth without losing contrast. Since this technique does not require the
ions to be confined in the Lamb-Dicke regime, thermal states with many phonons
should be sufficient for operation.
