Globular Clusters are remarkable witnesses of their host galaxy’s interaction and merger history. Our aim is to perform the photometric analysis of the Globular Cluster System of the giant elliptical NGC 4696, the brightest member of Centaurus, a rich and dynamically young galaxy cluster. We obtained deep Magellan $6.5$ m/MegaCam ($g'$, $r'$, $i'$) photometry, with which we identified a sample of $3818$ stellar clusters around NGC 4696 that are analyzed in the context of possible interactions and its assembly history. After carefully modeling and subtracting the galaxy light, we used selection criteria based on the shape, colors and magnitudes to identify globular cluster candidates. We find a number of features that indicate a disturbed Globular Cluster System that point towards a complex evolution with other neighbouring members of Centaurus. Formally, two subpopulations could be found at $(g'-i')_0 = 0.763 0.004$ and $(g'-i')_0=1.012 0.004$. Moreover, the color distribution does not show the presence of a significant blue-tilt, but it presents a trend with radius, where at small galactocentric distances a unimodal distribution is preferable to a bimodal one, suggesting the presence of an intermediate globular cluster population. Besides the color distribution, also the metallicity distribution shows a bimodal trend, with peaks at Fe/H 0.010$ and Fe/H 0.012$. The radial density profiles show different slopes for the blue and red populations and the azimuthal distributions are well fitted by an asymmetrical sinusoidal function, with peaks projecting towards two nearby galaxies, NGC 4696B and NGC 4709, indicating past interactions among these three galaxies. Finally, we derive a globular cluster specific frequency of $S_N=6.8 0.9$, in good agreement with the values obtained for other giant ellipticals and with previously estimated $S_N$ of NGC 4696. All these results point toward a complex globular cluster system, strongly influenced by the interaction history of NGC 4696 with the other galaxies of the Centaurus cluster. In a future work, the spectroscopic follow-up of the globular cluster candidates analyzed in this study and broadening the photometric baseline will allow us to highlight the formation and evolution of the entire Centaurus cluster.