Wide binary stars with similar components hosting planets provide an interesting opportunity for exploring the star-planet chemical connection. Here, we present a detailed characterization of the solar-type stars in the WASP-160 binary system. No planet has been reported yet around WASP-160A while WASP-160B is known to host a transiting Saturn-mass planet, WASP-160B b. For this planet, we also derive updated properties from both literature and new observations. Furthermore, using TESS photometry, we constrain the presence of transiting planets around WASP-160A and additional ones around WASP-160B. The stellar characterization includes, for the first time, the computation of high-precision differential atmospheric and chemical abundances based on high-quality spectra. Our analysis reveals evidence of a correlation between the differential abundances and the condensation temperatures of the elements. In particular, we find both a small but significant deficit of volatiles and an enhancement of refractory elements in WASP-160B relative to WASP-160A. After WASP-94, this is the second stellar pair among the shortlist of planet-hosting binaries showing this kind of anomalous chemical pattern. We discuss that the formation of WASP-160B b and late accretion of rocky material by its host star, likely triggered by the inward migration of this giant planet, could explain the observed chemical pattern. Alternative scenarios involve the formation of additional giant planets around WASP-160B and rocky objects around WASP-160A. Full details about this work can be found in Jofré et al. (2021; arXiv:2109.04590).