Context. X-shaped radio galaxies (XRGs) exhibit a pair of bright primary lobes and a pair of weak secondary lobes (“wings”), which are oriented with an angle that gives the structure a cross-like shape. Though several theoretical models have been proposed to explain their origin, there is currently not a general consensus on a formation scenario. Aims. We analysed new multifrequency Karl G. Jansky Very Large Array (JVLA) radio data at 1.5, 5.5, 6, and 9 GHz of the candidate XRG in Abell 3670 (A3670) in order to characterise and classify it for the first time and to investigate its origin. Methods. We produced flux, spectral index, and radiative age maps of A3670 by means of the new radio data. We investigated the connection between the radio galaxy and its host, a brightest cluster galaxy (BCG) with two optical nuclei classified as a dumbbell galaxy. Finally we discussed the literature models and compared them to the observed properties of A3670. Results. We classify A3670 as a Fanaroff–Riley I-type XRG and measured a 1.4 GHz radio power of P_1.4 = 1.7 × 10²⁵ W Hz⁻¹. By estimating the radiative age of the various source components, we find that the wings are Δt ≃ 20 Myr older than the lobes. We verified that the lobes and wings are aligned with the major and minor axes of the optical galaxy, respectively, and we estimated a black hole mass of M_BH ∼ 10⁹ M_⊙, which is in agreement with the typical properties of the XRGs. Conclusions. Among the discussed scenarios, the jet-shell interaction model may best reproduce the observed properties of A3670. The gas of a stellar shell is responsible for the deflection of the jets, thus forming the wings. The presence of stellar shells in A3670 is plausible, but it needs further optical observations to be confirmed.