X-ray beams carrying orbital angular momentum (OAM) are an emerging tool for probing matter. Optical elements, such as spiral phase plates and zone plates, have been widely used to generate OAM light. However, due to the high impinging intensities, these optics are challenging to use at X-ray free-electron lasers (XFELs). Here, we propose a self-seeded free-electron laser (FEL) method to produce intense X-ray vortices. Unlike passive filtering after amplification, an optical element will be used to introduce the helical phase to the radiation pulse in the linear regime, significantly reducing thermal load on the optical element. The generated OAM pulse is then used as a seed and significantly amplified. Theoretical analysis and numerical simulations demonstrate that the power of the OAM seed pulse can be amplified by more than two orders of magnitude, reaching peak powers of several tens of gigawatts. The proposed method paves the way for high-power and high-repetition-rate OAM pulses of XFEL light.