Complex-shaped light fields with specially designed intensity, phase, and polarization distributions are highly demanded for various applications including optical tweezers, laser material processing, and lithography. Here, we propose a novel (to the best of our knowledge) optical element formed by the twisting of a conic surface, a twisted microaxicon, allowing us to controllably generate high-quality spiral-shaped intensity patterns. Performance of the proposed element was analyzed both analytically and numerically using ray approximation and the rigorous finite difference time domain (FDTD) solution of Maxwell’s equation. The main geometric parameters, an apex cone angle and a degree of twisting, were considered to control and optimize the generated spiral-shaped intensity patterns. The three-dimensional structure of such a microaxicon cannot be described by an unambiguous height function; therefore, it has no diffraction analogue in the form of a thin optical element. Such an element can be produced via direct laser ablation of transparent targets with structured laser beams or direct laser writing via two-photon photopolymerization and can be used in various micro- and nano-optical applications.