  In models of minicharged dark matter associated with a hidden $U(1)$
symmetry, astrophysical black holes may acquire a "dark" charge, in such a way
that the inspiral dynamics of binary black holes can be formally described by
an Einstein-Maxwell theory. Charges enter the gravitational wave signal
predominantly through a dipole term, but their effect is known to effectively
first post-Newtonian order in the phase, which enables measuring the size of
the charge-to-mass ratios, $|q_i/m_i|$, $i = 1,2$, of the individual black
holes in a binary. We set up a Bayesian analysis to discover, or constrain,
dark charges on binary black holes. After testing our framework in simulations,
we apply it to selected binary black hole signals from the second Gravitational
Wave Transient Catalog (GWTC-2), namely those with low masses so that most of
the signal-to-noise ratio is in the inspiral regime. We find no evidence for
charges on the black holes, and place typical 1-$\sigma$ bounds on the
charge-to-mass ratios of $|q_i/m_i| \lesssim 0.2 - 0.3$.
