Based on nonlinear wave mixing, we experimentally propose a scheme for directly generating optical orbital angular momentum (OAM) by a spirally structured fundamental wave interacting with a nonlinear medium, in which the nonlinear susceptibilities are homogenous. In the experiment, the second-harmonic generation of a fundamental wave carrying positive (negative) integers and fractional OAM states was investigated. This study presents a convenient approach for dynamic control of OAM of vortex beams, which may feature their applications in optical manipulation and optical communication.