We present deep 3-GHz Karl G. Jansky Very Large Array (VLA) observations of the potentially recoiling black hole CID-42 in the Cosmic Evolution Survey (COSMOS) field. This galaxy shows two optical nuclei in the Hubble Space Telescope/Advanced Camera for Surveys (HST/ACS) image and a large velocity offset of ≈1300 km s^(−1) between the broad and narrow Hβ emission line although the spectrum is not spacially resolved (Civano et al. 2010). The new 3 GHz VLA data have a bandwidth of 2 GHz and to correctly interpret the flux densities imaging was done with two different methods: multiscale multifrequency (MSMF) synthesis and spectral windows (SPWs) stacking. The final resolutions and sensitivities of these maps are 0.7 arcsec with rms = 4.6 μJy beam^(−1) and 0.9 arcsec with rms = 4.8 μJy beam^(−1), respectively. With a 7σ detection, we find that the entire observed 3-GHz radio emission can be associated with the south-eastern component of CID-42, coincident with the detected X-ray emission. We use our 3 GHz data combined with other radio data from the literature ranging from 320 MHz to 9 GHz, which include the VLA, Very Long Baseline Array (VLBA) and Giant Metrewave Radio Telescope (GMRT) data, to construct a radio synchrotron spectrum of CID-42. The radio spectrum suggests a type I unobscured radio-quiet flat-spectrum active galactic nucleus (AGN) in the south-eastern component which may be surrounded by a more extended region of old synchrotron electron population or shocks generated by the outflow from the supermassive black hole (SMBH). Our data are consistent with the recoiling black hole picture but cannot rule out the presence of an obscured and radio-quiet SMBH in the north-western component.