Frequency-modulated continuous-wave (FMCW) synthetic aperture radar (SAR) is now a commonly adopted solution for producing high-resolution electromagnetic images of the earth surface. However, many SAR applications, such as detection or imaging of moving targets, have not yet been thoroughly researched for FMCW scenarios. This paper presents a refocusing technique that works in the wavenumber domain and is based on the reference spectrum of a point-like moving target. The method is illustrated using simulated experiments, and is further tested by processing real data collected by the Ka-band MIRANDA-35 sensor. The obtained results are validated and compared with independent ground measurements, thus demonstrating the accuracy of the presented method.