This Letter reports a new method for the generation of optical vortices using a micropatterned optical fiber tip. Here, a spiral phase plate (2π phase shift) is micromachined on the tip of an optical fiber using a focused ion beam. This is a high resolution method that allows milling the fibers with nanoscale resolution. The plate acts as a beam tailoring system, transforming the fundamental guided mode, specifically a Gaussian mode, into the Laguerre-Gaussian mode (LG01), which carries orbital angular momentum. The experimental results are supported by computational simulations based on the finite-difference time-domain method.