Comb-based optical arbitrary waveform measurement (OAWM) techniques can overcome the bandwidth limitations of conventional coherent detection schemes, thereby enabling ultra-broadband signal acquisition in a wide range of scien-tific and industrial applications. For efficient and robust implementation of such OAWM systems, miniaturization into chip-scale form factors is key. In this paper, we propose and demonstrate an OAWM scheme that exploits chip-scale Kerr soliton combs as compact and highly scalable multi-wavelength local oscillators (LO) and that does not require optical slicing filters, thus lending itself to efficient implementation on state-of-the-art high-index-contrast integration plat-forms such as silicon photonics. The scheme allows for measuring truly arbitrary waveforms with high accuracy based on a dedicated system model that is calibrated by means of a femtosecond laser with a known pulse shape. We demonstrate the viability of our approach in a proof-of-concept experiment by capturing optical waveforms with multiple 16QAM and 64QAM wavelength-division multiplexed (WDM) data signals, reaching overall line rates of up to 1.92 Tbit/s within an optical acquisition bandwidth of 610 GHz. To the best of our knowledge, this is the highest bandwidth that has so far been demonstrated in an OAWM experiment. Our work opens a path towards efficient implementation of OAWM systems, offering THz acquisition bandwidths in highly compact and robust assemblies that can rely on chip -scale frequency-comb generators and simple filter-less detector circuits. (c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement