This paper presents the introduction of Digital Twins in the case of an historic masonry tower for rapidly addressing earthquake-induced damage identification. In the context of the present paper, a digital twin is a model or a suite of models of the considered structure that are updated/modified during time based on monitoring data. In particular, the proposed approach combines Operational Modal Analysis (OMA), Surrogate Modeling (SM) and nonlinear Incremental Dynamic Analysis (IDA). On the one hand, OMA-based Structural Health Monitoring (SHM) systems successfully allow the detection of small structural damages occurring during earthquakes, and on the other, SM exploits the correlation between continuous vibration data and structural stiffnesses while IDA is carried out from a tuned model together with in situ recorded seismic data. The San Pietro bell tower has been considered for the validation of the proposed methodology. The tower is a monumental medieval masterpiece, located in Perugia, Italy, and it represents a relevant case study in the scientific literature due to its important experience during the 2016-2017 seismic sequence that occurred in Central Italy. While the OMA-vibration data processing assessed distinct earthquake-induced changes in its global dynamic behavior, the focus of the present work is the results on the use of linear as well as non-linear modeling, i.e. SM and IDA, respectively, aimed for post-earthquake damage localization and quantification.