In the construction of RCD (Roller-compacted Concrete) dams, two types of internal and external concrete are used; Thermal cracks are occurred due to hydration of various cements in this type of dams. Ignorance of this issue can lead to crack formation in the susceptible points of the dams. In this research, the behavior of the thermal cracks existed in the RCD dam body, is investigated through translational and rotational components of the earthquake. Three-dimensional finite element (FE) model of the concrete dam is built in ABAQUS software, and the model was subjected to 7 earthquake records. After validation of the model, the propagation of the crack existed in the dam body is evaluated using fracture mechanics criterion. The results of the finite element analysis show that the existence of the cracks in the susceptible points of the dam, leads to propagation of these cracks during an earthquake. Especially, with considering the rotational component of the earthquake which has the significant contribution in the obtained values of the crack propagation criterion; This contribution is related to the frequency content of the earthquake, which can lead to an increase of the crack propagation energy up to 50 percent in some earthquake records.