In recent years, the use of radar technology has been proposed in a wide range of subsurface imaging applications. Traditionally, linear scan trajectories are used to acquire data in most subsurface radar applications. However, novel applications, such as breast microwave imaging and wood inspection, require the use of nonlinear scan trajectories in order to adjust to the geometry of the scanned area. This paper proposes a novel reconstruction algorithm for subsurface radar data acquired along cylindrical scan trajectories. The spectrum of the collected data is processed in order to locate the spatial origin of the target reflections and remove the spreading of the target reflections which results from the different signal travel times along the scan trajectory. The proposed algorithm was successfully tested using experimental data collected from phantoms that mimic high contrast subsurface radar scenarios, yielding promising results. Practical considerations such as spatial resolution and sampling constraints are discussed and illustrated as well.