We theoretically and numerically demonstrate the generation of a relativistic modified Bessel-Gaussian beam (MBGB) via plasma-based beam braiding. It is realized by injecting several intense Gaussian pulses with well-designed offsets and angles into an underdense plasma channel which acts as a laser-pulse combiner via refractive coupling. The MBGB propagates stably in the plasma channel with a well-controlled orbital angular momentum of large value, exciting a twisted plasma wave. After leaving the plasma, it becomes unguided and survives in vacuum for at least hundreds of femtoseconds. This method is insensitive to the initial laser injection conditions and thus should be robust for experimental implementation. It provides an alternative approach in generating high-quality tunable intense optical vortex beams which are desired for various applications.