Spintronics aims at extending the possibility of conventional electronics by using not only the charge of the electron, but also its spin. The resulting spintronic devices, combining the front-end CMOS technology of electronics with a magnetic backend technology, employ Magnetic Tunnel Junctions (MTJs) as core elements. With the intent of simulating a circuit without fabricating it first, a reliable MTJ electrical model which is applicable to the standard SPICE (Simulation Program with Integrated Circuit Emphasis) simulator is required. Since such a model was lacking so far, we present an accurate MTJ SPICE model whose magnetic state is written by using the Spin-Transfer Torque (STT) effect. This model has been developed in C language and validated on the Cadence Virtuoso Platform with Spectre simulator. Its operation is similar to those of the standard BSIM (Berkeley Short-channel IGFET Model) SPICE model of the MOS transistor and fully compatible with the SPICE electrical simulator. In order to illustrate the model performance, we studied the tunneling conductance and STT-driven magnetization dynamics by comparing our simulation results with theoretical macrospin calculations and results found in the literature.