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Yep. In fact there’s a process called inverse Compton scattering that essentially works this way. In ordinary Compton scattering, a photon scatters off a stationary electron and typically leaves with less energy (since the electron gets a kinetic kick). In inverse Compton scattering, a photon collides with a moving electron which can cause the photon to gain energy.
One application of this is to produce gamma-ray beams. You take a beam of light (often from a laser) and collide it head on with a beam of relativistic electrons traveling in the opposite direction. In the electron rest frame, the photon has gamma-ray energy, while in the lab frame it might only be visible light. The back-scattered photon can then be boosted to the gamma regime in the lab frame, and now you’ve got a gamma-ray beam.
I just want know when my giant fission-powered robot can finally be armed with nuclear-pumped gamma lasers.