Aiming at the problems of the current OAM antenna, such as fewer modes, and difficulty to conform, this paper designs a terahertz-frequency array antenna using graphene and MXene. By adjusting the feeding phase, different OAM vortex wave modes can be generated. Changing the external voltage, the conductivity of graphene is modified, thus, the operating frequency can be tunable. The impact of bending on antenna performance is also studied, and phase and frequency compensation methods are proposed accordingly. The simulation results show that the antenna can generate numerous OAM vortex waves with integer mode of 0~3 and fractional mode of 0.5、1.5、2.5 by simply adjusting the feeding phase difference. The antenna gain can reach 11.7 dBi, and the operating frequency can be tuned within the range of 1.1~1.9 THz. For significant cylindrical bending, the proposed phase and frequency compensation methods can effectively maintain the vortex wave form and operating frequency. According to the experimental results, the proposed flexible OAM antenna is very promising in applications of antenna deformation and bending scenarios, such as human-machine interfaces, soft robots, and aerospace components, etc.