We present a protocol for rotation measurement via matter-wave Sagnac interferometry using trapped ions. The ion trap based interferometer encloses 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 contrast loss. Since this technique does not require the ions to be confined in the Lamb–Dicke regime, Doppler laser cooling should be sufficient to reach a sensitivity of ##IMG## [http://ej.iop.org/images/0953-4075/50/6/064002/jpbaa5a8fieqn1.gif] {${ \mathcal S }=1.4\times {10}^{-6}\,{\rm{rad}}\,{{\rm{s}}}^{-1}\,{{\rm{H}}{\rm{z}}}^{-1/2}$} .