We theoretically discuss an implementation of a Sagnac interferometer with cold atoms. In contrast to currently existing schemes our protocol does not rely on any free propagation of atoms. Instead it is based on superpositions of fully confined atoms and state-dependent transport along a closed path. Using Ramsey sequences for an atomic clock, the accumulated Sagnac phase is encoded in the resulting population imbalance between two internal (clock) states. Using minimal models for the above protocol we analytically quantify limitations arising from atomic dynamics and finite temperature. We discuss an actual implementation of the interferometer with adiabatic radio-frequency potentials that is inherently robust against common mode noise as well as phase noise from the reference oscillator. ; Comment: 5 pages, 2 figures