The development of ultra-intense and ultra-short light sources is currently a subject of intense research driven by the discovery of novel phenomena in the realm of relativistic optics, such as the production of ultrafast energetic particle and radiation beams for applications. It has been a long-standing challenge to unite two hitherto distinct classes of light sources:those achieving relativistic intensity and those with pulse durations approaching a single light cycle. While the former class traditionally involves large-scale amplification chains, the latter class places high demand on the spatiotemporal control of the electromagnetic laser field. Here, we present a light source producing waveform-controlled 1.5-cycle pulses with a 719 nm central wavelength that can be focused to relativistic intensity at a 1 kHz repetition rate based on nonlinear post-compression in a long hollow-core fiber. The unique capabilities of this source allow us to observe the first experimental indications of light waveform effects in laser wakefield acceleration of relativistic energy electrons.