Tin sulfide doped with copper (SnS:Cu) thin films were deposited on glass substrates by the ultrasonic spray pyrolysis (USP) technique at different concentration ratios (y = [Cu]/[Sn] = 0% (undoped), 2%, 5% and 10%). The aim of this work is to analyze the effect of copper on structural, morphological, and optoelectronic properties of SnS:Cu and discuss their possible application as an absorber layer in a solar cell structure proposed which is simulated using SCAPS software. X-ray diffraction (XRD) reveals an orthorhombic structure in the undoped sample and a cubic structure in doped ones. Raman spectroscopy suggests a possible unit cell size change due to the addition of Cu. Scanning electron microscopy (SEM) shows growth in grain density with an increasing y. Image analysis based on second-order features was used to discuss grain distribution. UV-VIS spectroscopy helps to find an increase of bandgap for the doped samples when copper concentration increases, going from 1.82 eV in the doped film y = 2% to 2.2 eV in the 10% doped samples. A value of 3.51 eV was found for the undoped sample y = 0%. A rise in both carrier concentration and mobility but a decrease in resistivity when y is increased was observed through the Hall–Van der Pauw technique. Simulations by SCAPS helped conclude that considering the material thickness, the SnS:Cu compound can be an alternative for implementation in the manufacturing of solar cells as an absorber layer since it is possible to obtain the optoelectronic properties necessary using the UPS economical technique.