We report on the quantum electrodynamical analog of a Sagnac phase induced by the fast rotation of a neutral nanoparticle onto atomic waves propagating in its vicinity. The quantum vacuum Sagnac phase is a geometric Berry phase proportional to the angular velocity of rotation. The persistence of a noninertial effect into the inertial frame is also analogous to the Aharonov-Bohm effect. Here, a rotation confined to a restricted domain of space gives rise to an atomic phase even though the interferometer is at rest with respect to an inertial frame. By taking advantage of a plasmon resonance, we show that the magnitude of the induced phase can be close to the sensitivity limit of state of the art interferometers. The quantum vacuum Sagnac atomic phase is a geometric footprint of a dynamical Casimir-like effect.