  Quantum information processing with geometric features of quantum states may
provide promising noise-resilient schemes for quantum metrology. In this work,
we theoretically explore phase-space geometric Sagnac interferometers with
trapped atomic clocks for rotation sensing, which could be intrinsically robust
to certain decoherence noises and reach high precision. With the wave guide
provided by sweeping ring-traps, we give criteria under which the well-known
Sagnac phase is a pure or unconventional geometric phase with respect to the
phase space. Furthermore, corresponding schemes for geometric Sagnac
interferometers with designed sweeping angular velocity and interrogation time
are presented, and the experimental feasibility is also discussed. Such
geometric Sagnac interferometers are capable of saturating the ultimate
precision limit given by the quantum Cram\'er-Rao bound.
