  Self-interacting scalar field dark matter can be seen as an extension of the
free case known as Fuzzy dark matter. The interactive case is capable of
reproducing the positive features of the free case at both astrophysical and
cosmological scales. On the other hand, current imaging black holes (BHs)
observations provided by the Event Horizon Telescope (EHT) collaboration cannot
rule out the possibility that BHs can carry some amount of charge. Motivated by
these aspects, and by the possibility of detecting dark matter through its
gravitational imprints on BH observations, in this paper, we extend previous
studies of accretion of self-interacting scalar field dark matter to the
charged BH case. Our analysis is based on the assumption on spherically
symmetric flow and employs a test fluid approximation. All analytical
expressions are derived from the ground up in Schwarzschild coordinates.
Concretely, we implement analytical and numerical approaches to investigate the
impact of the charge on the energy flux. From this analysis, we notice that the
mass accretion rate efficiency is reduced up to $\sim 20\%$ for the maximum
allowed charge. Additionally, considering the mass accretion rate of
M87$^{\star}$ inferred from Polarization data of the EHT, we infer the
conservative bound $ \lambda_4 > (1.49-10.2)( m / 1 \rm {eV} )^4$ based on the
simple criterion that ensures the mass accretion rate caused by DM remains
subdominant compared to the baryonic component.
