We present a modified vat photopolymerization process for realizing novel fiber-reinforced composite parts wherein continuous fibers are selectively positioned and oriented across multiple layers along the build direction. This is in contrast to laminates and fiber-wound parts made by repeating fiber patterns; and additively manufactured parts with fibers inserted a posteriori or co-extruded selectively. Our process endows two benefits to the parts made with it: (i) spatially steered fibers embedded along specific paths inside to increase stiffness and strength; and (ii) in-situ fiber-matrix interface concurrently cured with matrix material as opposed to the matrix-matrix interface that exists in co-extruded fibers. The process is enabled by a robot manipulator that guides the fiber in each layer by incrementally orienting it along the tangential direction to the bespoke path. The robot arm and the end-effector do not obstruct the UV light source as they pull the fiber taut from afar in multiple directions to alleviate the undesirable effects of shadows. The robot arm is integrated with the build platform and the UV projector, and the entire process is automated. Examples that illustrate making parts with single and multiple fibers are presented to show the efficacy of the process and the machine. An example is shown with continuous fibers embedded along a few spatially varying principal-stress-flow paths inside a part to improve its stiffness and strength. An increase of 71 % in stiffness and 90 % in strength of the part is observed at fiber volume fraction as small as 0.39 %.