  Transport property under metallic ferroaxial ordering in an external magnetic
field is theoretically investigated. After presenting the relation between the
magnetoconductivity tensor and ferroaxial moment from the symmetry viewpoint,
we analyze the behavior of the unconventional Hall effect and
magnetoconductivity for a general five $d$-orbital tight-binding model under
the point group $C_{\rm 4h}$, where the ferroaxial moment is activated. We show
that the crystalline electric field that arises from the symmetry reduction
from $D_{\rm 4h}$ to $C_{\rm 4h}$ is essential for the ferroaxial-related
magnetotransport, while the relativistic spin-orbit coupling is not required.
We also compare the unconventional Hall effect driven by the ferroaxial moment
with the conventional Hall effect, the latter of which does not require the
ferroaxial moment. The present results provide characteristic transport
properties in the ferroaxial systems, which can be observed in various
candidate materials like Ca$_5$Ir$_3$O$_{12}$.
