Graphene antennas operating at mm-wave and THz frequencies enable miniaturization by being smaller than its metallic counterparts, while additionally providing frequency tunability capabilities. These characteristics are interesting for 6G short-range communication applications, where the antenna size is still one of the largest and, consequently, costly components inside a chip. In this work, a tunable planar antenna for operation at terahertz frequencies based on a graphene stack is proposed and analyzed. The proposed antenna consists of a stack of two graphene patches separated by a thin dielectric to provide higher efficiency and gain. This concept can broadly be applied to future THz communication systems because it can directly be integrated into transceiver units by being compatible with CMOS processes and manufacturing techniques. We use a full-wave electromagnetic solver to evaluate and compare the performance of this antenna to a simple graphene patch antenna in the range of 220 - 325 GHz. The results show that an increase in efficiency and gain can be accomplished. We also demonstrate the frequency tuning possibility of the antenna, which can be achieved by the electric field effect in the graphene stack by applying a bias voltage between the two graphene sheets.