  The identification of the topological invariant of a topological system is
crucial in experiments. However, due to the inherent non-Hermitian features,
such determination is notably challenging in non-Hermitian systems. Here, we
propose that the magnetic effect can be utilized to measure the Chern number of
the non-Hermitian Chern insulator. We find that the splitting of non-Hermitian
bands under the magnetic field is Chern number dependent. Consequently, one can
easily identify the Chern number by analyzing these splitting sub-bands. From
the experimental perspective, the measurement of non-Hermitian bands is
demonstrated in LC electric circuits. Furthermore, we find that the
non-Hermiticity can drive open (closed) orbits of sub-bands in the Hermitian
limit closed (open), which can also be identified by our proposal. These
phenomena highlight the distinctive capabilities of non-Hermitian systems. Our
results facilitate the detection of Chern numbers for non-Hermitian systems and
may motivate further studies of their topological properties.
