We have developed an auto-picking algorithm that is designed to automatically detect subsurface diffractors within ground-penetrating radar (GPR) data sets, to accurately track the hyperbolic diffractions originating from the identified scatterers, and to recover the subsurface electromagnetic (EM) velocity distribution, among other possible analyses. Our procedure presents several advantages with respect to other commonly applied diffraction tracking techniques because it can be applied with minimal signal preprocessing, thus making it more versatile and adaptable to local conditions; it requires only limited input from the interpreter in the form of a few thresholds for the tracking parameters, thus making the results more objective; and it does not involve pretraining as opposed to machine-learning algorithms, thus removing the need to gather a large and comprehensive image database of all possible subsurface situations, which would not necessarily be limited to only examples of diffractions. The presented algorithm starts by identifying those signals that are likely to belong to diffraction apexes, which are then used as initial seeds by the auto-tracking process. The horizontal search window used during the auto-tracking process is locally adapted through a rough preliminary estimate of the size of each diffraction. In addition, multiple seeds within the same apex can produce several acceptable hyperbolas tracking the same diffraction phase. The algorithm thus selects the best-fitting ones by assessing several signal attributes while also removing redundant hyperbolas and the expected false positives. The algorithm is applied to two glaciological GPR profiles, and it is able to accurately track the vast majority of the recorded diffractions, with very few false positives and negatives. This produces a statistically sound EM velocity distribution, which was used to assess the state of the surveyed alpine glacier.