We present large-scale (~2000 arcmin^2), deep (~20 μJy), high-resolution (~1") radio observations of the Ophiuchus star-forming complex obtained with the Karl G. Jansky Very Large Array at λ = 4 and 6 cm. In total, 189 sources were detected, 56 of them associated with known young stellar sources, and 4 with known extragalactic objects; the other 129 remain unclassified, but most of them are most probably background quasars. The vast majority of the young stars detected at radio wavelengths have spectral types K or M, although we also detect four objects of A/F/B types and two brown dwarf candidates. At least half of these young stars are non-thermal (gyrosynchrotron) sources, with active coronas characterized by high levels of variability, negative spectral indices, and (in some cases) significant circular polarization. As expected, there is a clear tendency for the fraction of non-thermal sources to increase from the younger (Class 0/I or flat spectrum) to the more evolved (Class III or weak line T Tauri) stars. The young stars detected both in X-rays and at radio wavelengths broadly follow a Güdel-Benz relation, but with a different normalization than the most radioactive types of stars. Finally, we detect a ~70 mJy compact extragalactic source near the center of the Ophiuchus core, which should be used as gain calibrator for any future radio observations of this region.