Surface texture, as an important surface engineering technique, can enhance the tribological properties of contact surfaces. This work presents an experimental investigation of the fretting wear behavior of silicone rubber films with a biomimetic surface texture under a spherical indenter. Inspired by human fingerprints and tree frog toe pads, hexagonal loop textures with three different texture spacings are created on the surface of silicone rubber films. Three types of indenters are considered: stainless steel, polypropylene, and silicone rubber. The impacts of the texture spacing, displacement amplitude, normal force, frequency, and indenter material on the fretting wear behavior are discussed in detail. The wear volume was measured via a three-dimensional white light profiler. The surface wear morphology and fretting wear mechanism of the textured surfaces were analyzed by scanning electron microscopy. Adding a surface texture can effectively decrease the coefficient of friction (COF) of silicone rubber. In addition, the smaller the texture spacing is, the more pronounced the COF decreases and the lower the specific wear rate.