We propose an alternative route to engineer Majorana zero modes (MZMs), which relies on inducing shift or spin vortex defects in magnetic textures which microscopically coexist or are in proximity to a superconductor. The present idea applies to a variety of superconducting materials and hybrid structures, irrespectively of their spin-singlet, -triplet, or mixed type of pairing, as long as their bulk energy spectrum contains robust point nodes. Our mechanism provides a new framework to understand the recent observations of pairs of MZMs in superconductor - magnetic adatom systems. Moreover, it can inspire the experimental development of new platforms, consisting of nanowires in proximity to conventional superconductors with strong Rashba spin-orbit coupling.