Tremendous efforts have been devoted to the modeling of droplet deposition on smooth and patterned surfaces with ordered structures. However, systematic work focusing on randomly rough surfaces, which are the most common bare substrate surfaces, can be hardly identified. A phase field modeling method together with a unique analysis approach has been developed in this work to characterize single droplet deposition on randomly rough surfaces. It is interesting to observe that the droplet shape evolves quite differently on a randomly rough surface, as compared to a patterned surface, even if two surfaces have the same roughness. Parametric studies have been carried out to explore how the morphological metrics of randomly rough surfaces, which include the Wenzel roughness parameter (W-r) and the root-mean-square roughness (R-r), can affect droplet impact dynamics. The quantitative relationships derived from this study can eventually shed light on droplet shape on-aim control during the deposition process, which is of great practical importance in many applications.