The present experimental study is devoted to examination of the vortex receptivity mechanism associated with excitation of unsteady cross-flow (CF) waves due to scattering of unsteady free-stream vortices on localized steady surface non-uniformities (roughness). The measurements are carried out in a low-turbulence wind tunnel by means of a hot-wire anemometer in a boundary layer developing over a $25\textdegree $ swept-wing model. The harmonic-in-time free-stream vortices were excited by a thin vibrating wire located upstream of the experimental-model leading edge and represented a kind of small-amplitude von Kármán vortex street with spanwise orientation of the generated instantaneous vorticity vectors. The controlled roughness elements (the so-called ‘phased roughness’) were placed on the model surface. This roughness had a special shape, which provided excitation of CF-waves having basically some predetermined (required) spanwise wavenumbers. The linearity of the stability and receptivity mechanisms under study was checked accurately by means of variation of both the free-stream-vortex amplitude and the surface roughness height. These experiments were directed to obtaining the amplitudes and phases of the vortex-roughness receptivity coefficients for a number of vortex disturbance frequencies. The vortex street position with respect to the model surface (the vortex offset parameter) was also varied. The receptivity characteristics obtained experimentally in Fourier space are independent of the particular roughness shape, and can be used for validation of receptivity theories.