We present a data-driven method for the synthetic generation of wall roughness of additively manufactured (AM) surfaces. The method adapts Rogallo’s synthetic turbulence method (Rogallo in Numerical experiments in homogeneous turbulence, Nasa Technical Memorandum 81315, National Aeronautics and Space Administration, 1981) to generate correlated Fourier modes from data extracted from an electron microscope image. The fields are smooth and compatible with grid generators in computational fluid dynamics or other numerical simulations. Unlike machine learning methods that require more than 20 scans of surface roughness for training, this new method can generate an infinite amount of synthetic roughness fields to any desired spatial domain size, using a single input image. Five types of synthetic roughness fields are tested, based on an input roughness image from literature. A comparison of their spectral energy and two-point correlations shows that a synthetic vector component that aligns with the AM laser path closely approximates the roughness structures of the scan. The synthetic roughness is used in a discontinuous Galerkin laminar boundary-layer simulation, demonstrating the new approach’s ease of integration into CFD applications.