  There is growing interest in the photo-induced generation of rectified
current, namely photocurrent phenomenon. While the response was attributed to
noncentrosymmetric structures of crystals, the parity violation accompanied by
the magnetic ordering, that is, magnetic parity violation, is recently
attracting attention as a platform for a photocurrent generator. In this paper,
we investigate the photocurrent response in the current-ordered phase,
realizing the magnetic parity violation without the spin degree of freedom,
although prior studies focused on the parity-violating spin structure. The
loop-current order breaks the inversion symmetry while preserving the
parity-time-reversal symmetry. With a model of Sr$_2$IrO$_4$, we demonstrate
the linearly and circularly polarized light-induced photocurrent responses in
the current-ordered state. Each photocurrent has a distinct tolerance of the
scattering rate according to the mechanism for the photocurrent creation. The
predicted photocurrent response is comparable to that in prototypical
semiconductors. We propose a probe to detect the hidden-ordered phase in
Sr$_2$IrO$_4$ by the photocurrent response.
