The radiation-pressure coupling between two harmonic oscillators has been used in optomechanics for breakthrough experiments in the control and detection of mechanical displacement. Used primarily in optomechanics, there have been few reports of exploiting such a type of interaction in other platforms. Here, we engineer two superconducting LC circuits coupled by a strong photon-pressure interaction, a term we use in analogy to the radiation-pressure interaction between light and mechanical objects. The coupling arises from a change in the resonant frequency of one circuit in response to the current flowing in the second. We observe dynamical backaction between the two circuits, photon-pressure-induced transparency and absorption, and enter the strong coupling regime. Furthermore, we observe parametrically amplified thermal current fluctuations in a radiofrequency circuit close to its quantum ground state. Owing to the high design flexibility of superconducting circuits, our approach will enable new experiments with radiofrequency photons and parameter regimes of photon-pressure coupling that are not accessible in other platforms.