We present a non-iterative holographic technique for efficient and versatile laser beam shaping along arbitrary 3D curves. Light beams with intensity shaped for several 3D curves: Tilted ring, Viviani’s curve, Archimedean spiral, and trefoil-knotted curve have been experimentally generated and applied for optical trapping of micrometer-sized dielectric particles. The high intensity gradients and independent phase control prescribed along the curve make this kind of laser trap attractive for multiple particle manipulation and allow for forward and backward motion to the light source. Indeed, different configurations of tractor beam traps are experimentally demonstrated. This technique can also be applied for laser micro-machining.