  We consider the ratchet dynamics in a $\mathcal{PT}$-symmetric Floquet
quantum system with symmetric temporal (harmonic) driving. In the exact
$\mathcal{PT}$ phase, for a finite number of resonant frequencies, we show that
the long-lasting resonant currents can be generated with the symmetric
time-continuous driving, which would otherwise forbid the generation of
directed currents in the Hermitian limit. Such a non-Hermitian resonant current
can be enhanced by increasing the non-Hermitian level, and in particular, the
resonant current peaks (reaches the largest negative value) under the condition
that the imaginary part of the potential depth is equal to the real part, at
which the stable asymptotic current occurs owing to exceptional points (EPs)
mechanism. Moreover, the directed currents originating from the symmetry
breaking are reported, which increase linearly with the driving frequency, the
mechanism behind which is that the cutoff of the momentum eigenstates for the
Floquet state with maximum imaginary quasienergy increases as the driving
frequency is continuously increased. We also present a non-Hermitian
three-level model that can account for the resonant currents and gives
surprisingly good agreement with direct numerical results for weak driving,
even in the $\mathcal{PT}$-broken regime for the first-order resonance. Our
results provide a new means of realizing the non-Hermiticity-controlled ratchet
current by means of a smooth continuous driving, previously used only to
generate currents in Hermitian systems.
