We report on a vortex laser chirped-pulse amplification (CPA) system that delivers pulses with a peak power of 45 TW. A focused intensity exceeding 1019 W/cm2 has been demonstrated for the first time by the vortex amplification scheme. Compared with other schemes of strong-field vortex generation with high energy flux but narrowband vortex-converting elements at the end of the laser, an important advantage of our scheme is that we can use a broadband but size-limited q-plate to realize broadband mode-converting in the front end of the CPA system, and achieve high-power amplification with a series of amplifiers. This method is low cost and can be easily implemented in an existing laser system. The results have verified the feasibility to obtain terawatt and even petawatt vortex laser amplification by a CPA system, which has important potential applications in strong-field laser physics, for example, generation of vortex particle beams with orbital angular momentum, fast ignition for inertial confinement fusion and simulation of the extreme astrophysical environment.