  We implement circuit quantum electrodynamics (cQED) with quantum dots in
bilayer graphene, a maturing material platform for semiconductor qubits that
can host long-lived spin and valley states. The presented device combines a
high-impedance ($Z_\mathrm{r} \approx 1 \mathrm{k{\Omega}}$) superconducting
microwave resonator with a double quantum dot electrostatically defined in a
graphene-based van der Waals heterostructure. Electric dipole coupling between
the subsystems allows the resonator to sense the electric susceptibility of the
double quantum dot from which we reconstruct its charge stability diagram. We
achieve sensitive and fast detection with a signal-to-noise ratio of 3.5 within
1 ${\mu}\mathrm{s}$ integration time. The charge-photon interaction is
quantified in the dispersive and resonant regimes by comparing the
coupling-induced change in the resonator response to input-output theory,
yielding a maximal coupling strength of $g/2{\pi} = 49.7 \mathrm{MHz}$. Our
results introduce cQED as a probe for quantum dots in van der Waals materials
and indicate a path toward coherent charge-photon coupling with bilayer
graphene quantum dots.
