We demonstrate that antiskyrmions can serve as magnetic quadrupole lenses that focus or defocus electric currents traversing them. We showcase the antiskyrmion core as a focal point where electron beams converge for specific injection directions, leading to anisotropic and nonuniform current distributions. Thus the current-induced antiskyrmion dynamics is profoundly modified by the magnetic quadrupole lensing via the spin-transfer torque. By incorporating quantum transport and micromagnetic simulations iteratively, we self-consistently capture the coupled dynamics of conduction electrons and antiskyrmions. Our results unveil a quadrupolar antiskyrmion Hall effect that is highly anisotropic with respect to the current direction and can be effectively tuned by the spin-orbit coupling. In particular, the current focusing (defocusing) dramatically enhances (suppresses) the antiskyrmion speed while simultaneously reducing its Hall angle, thereby overcoming a key challenge for antiskyrmion racetrack memories. Our work establishes the intrinsic current lensing as a powerful mechanism for manipulating topological magnetic textures and opens new avenues for antiskyrmion-based spintronic devices.