Achieving highly tailored control over both the spatial and temporal evolution of light's orbital angular momentum (OAM) on ultrafast timescales remains a critical challenge in photonics. Here, we introduce a method to modulate the OAM of light on a femtosecond scale by engineering a space-time coupling in ultrashort pulses. By linking azimuthal position with time, we implement an azimuthally varying Fourier transformation to dynamically alter light's spatial distribution in a fixed transverse plane. Our experiments demonstrate self-torqued wave packets that exhibit spiraling motions and rapid temporal OAM changes down to a few femtoseconds. We further extend this concept to generate angularly self-accelerating wave packets that adjust their OAM by redistributing their energy density across their spectral bandwidth, without external forces. The ability to tune the spatial-temporal properties of light on demand opens the possibility for exploring ultrafast light dynamics at fundamental timescales, with far-reaching implications for ultrafast spectroscopy, nano- and microstructure manipulation, condensed matter physics, and other related areas.