Electromagnetic waves with a helical-like wavefront are known as optical vortices. One of their main characteristics is a phase structure that has a circulation around a singularity and that they carry orbital angular momentum (OAM). OAM is a fundamental property that governs the interaction of these sources with matter. In the present paper, we study the electron dynamics driven by a so-called spatiotemporal optical vortex (STOV). Contrary to the conventional optical vortices, a STOV carries transverse OAM. By designing a streakinglike technique, we aim to fully characterize the OAM of the STOV. Using both quantum mechanical and semiclassical models, we are able to dissect the spatially resolved photoelectron energy spectra and accurately retrieve the OAM. Our approach paves the way toward a complete understanding of the interaction of complex spatiotemporal light fields with atomic targets.