We report the single-cycle optical control of a freely propagating electron beam with an isolated cycle of midinfrared light. In particular, we produce and characterize a modulated electron current with peak-cycle-specific subfemtosecond structure in time. The direct effects of the carrier-envelope phase, amplitude, and dispersion of the optical waveform on the temporal composition, pulse durations, and chirp of the free-space electron wave function demonstrate the subcycle nature of our control. These results and concept may create novel opportunities in free-electron lasers, laser-driven particle accelerators, ultrafast electron microscopy, and wherever else high-energy electrons are needed with the temporal structure of single-cycle light.