Binary stars hosting exoplanets are a unique laboratory where chemical tagging can be performed to measure with high accuracy the elemental abundances of both stellar components, with the aim to investigate the formation of planets and their subsequent evolution. Here, we present a high-precision differential abundance analysis of the XO-2 wide stellar binary based on high resolution HARPS-N@TNG spectra. Both components are very similar K-dwarfs and host planets. Since they formed presumably within the same molecular cloud, we expect they should possess the same initial elemental abundances. We investigate if the presence of planets can cause some chemical imprints in the stellar atmospheric abundances. We measure abundances of 25 elements for both stars with a range of condensation temperature $T_{rm C}=40-1741$ K, achieving typical precisions of $sim 0.07$ dex. The North component shows abundances in all elements higher by $+0.067 pm 0.032$ dex on average, with a mean difference of +0.078 dex for elements with $T_{rm C} > 800$ K. The significance of the XO-2N abundance difference relative to XO-2S is at the $2sigma$ level for almost all elements. We discuss the possibility that this result could be interpreted as the signature of the ingestion of material by XO-2N or depletion in XO-2S due to locking of heavy elements by the planetary companions. We estimate a mass of several tens of $M_{oplus}$ in heavy elements. The difference in abundances between XO-2N and XO-2S shows a positive correlation with the condensation temperatures of the elements, with a slope of $(4.7 pm 0.9) times 10^{-5}$ dex K$^{-1}$, which could mean that both components have not formed terrestrial planets, but that first experienced the accretion of rocky core interior to the subsequent giant planets.
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