Altermagnets constitute a novel, third fundamental class of collinear magnetic ordered materials, alongside with ferro- and antiferromagnets. They share with conventional antiferromagnets the feature of a vanishing net magnetization. At the same time they show a spin-splitting of electronic bands, just as in ferromagnets, caused by the atomic exchange interaction. On the other hand, topology has recently revolutionized our understanding of condensed matter physics, introducing new phases of matter classified by intrinsic topological order. Here we connect the worlds of altermagnetism and topology, showing that the electronic structure of the altermagnet CrSb is topological. Using high-resolution angle-resolved photoemission spectroscopy, we observe the large momentum-dependent spin-splitting in CrSb that induces altermagnetic Weyl nodes. We observe the related topological Fermi-arcs, which in electronic structure calculations are spin polarized. This indicates that in altermagnets the large energy scale intrinsic to their spin-splitting creates its own realm of robust electronic topology.