  Primordial black holes (PBHs) can answer a plethora of cosmic conundra, among
which the origin of the cosmic magnetic fields. In particular, supermassive
PBHs with masses $M_\mathrm{PBH}>10^{10} M_\odot$ and furnished with a
plasma-disk moving around them can generate through the Biermann battery
mechanism a seed primordial magnetic field which can later be amplified so as
to provide the magnetic field threading the intergalactic medium. In this work,
we derive the gravitational wave (GW) signal induced by the magnetic
anisotropic stress of such a population of magnetised PBHs. Interestingly
enough, by using GW constraints from Big Bang Nucleosynthesis (BBN) and an
effective model for the galactic/turbulent dynamo amplification of the magnetic
field, we set a conservative upper bound constraint on the abundances of
supermassive PBHs at formation time, $\Omega_\mathrm{PBH,f}$ as a function of
the their masses, namely that $\Omega_\mathrm{PBH,f}\leq 2.5\times
10^{-10}\left(\frac{M}{10^{10}M_\odot}\right)^{45/22}$. Remarkably, these
constraints are comparable, and, in some mass ranges, even tighter compared to
the constraints on $\Omega_\mathrm{PBH,f}$ from large-scale structure (LSS)
probes; hence promoting the portal of magnetically induced GWs as a new probe
to explore the enigmatic nature of supermassive PBHs.
