In-process monitoring of weld penetration depth is possible with optical coherence tomography (OCT). The weld depth can be identified with OCT by statistical signal processing of the raw OCT signal and keyhole mapping. This approach is only applicable to stable welding processes and requires a time-consuming keyhole mapping to identify the optimal placement of a singular OCT measuring beam. In this work, we use an OCT measurement line for the identification of the weld depth. This approach shows the advantage that the calibration effort can be reduced as the measurement line requires only calibration in one dimension. As current literature focuses on weld depth measurement with a singular measurement point in the keyhole, no optimal algorithm exists for weld depth measurement with an OCT measurement line. We developed seven different weld depth processing pipelines and tested these algorithms under different weld conditions, such as stable deep penetration welding, unstable deep penetration welding, and heat conduction welding. We analyzed the accuracy of the weld depth processing algorithms by comparing the measured weld depth with metallographic weld depths. The intensity accumulation approach is identified as the most accurate algorithm for successful weld depth measurement with a scanning OCT measurement line.