Non-spherical hydrogel particles are of fundamental interest and can find use in a variety of applications ranging from pharmaceuticals to biomedical to food. Here, we report a new method that leverages the yield stress property of viscoplastic fluids to synthesize shape-engineered alginate particles. By dripping an aqueous viscoplastic solution composed of sodium alginate and a yield-stress material into an ionic gelation bath, droplets are controllably deformed and crosslinked, producing a wide assortment of shapes. We find that by tuning the yield stress of the solution and the nozzle tip orientation, a range of shapes from symmetric and near-spherical, to asymmetric and anisotropic (e.g., egg-, rice grain-, arc-, ring-, snail shell-, tear-, and tadpole-like) can be produced. We explain our observations using scaling analysis of the forces exerted on the droplet at different stages of particle production. We show that the main factors that determine the degree of droplet deformation during bath entry and the final appearance of the alginate particles are the initial shape of the droplets, the timescales of the viscoplastic fluid relaxation versus the crosslinking reaction, and the physico-chemical properties of the yield-stress material.