In this study, the assessment of the possibility of imparting anisotropic tribological properties to medical silicone surfaces using laser surface texturing was performed. The transversal-shaped microgrooves were laser-textured on the surface of the silicone samples applying different angles of incidence of the laser beam (α) ranging from 0° to 40°. The surface characteristics of the laser-textured silicone surface were performed by optical microscopy, surface 3D topography measurements, and contact angle measurements; the tribological tests were carried out under technically dry friction conditions and friction with lubrication conditions. The results showed: a significant increase in surface texture parameters values with Sq values ranging from 7.57 µm for α = 0° to 36.9 µm for α = 10°, compared to the non-textured sample 1.52 µm, increased hydrophilicity of the textured surfaces for most samples demonstrated by contact angle measured values for α = 0° sample showing the largest contact angle 126° as compared to the non-textured samples 103°. The produced anisotropic microstructure of the textured silicone surface, i.e. its directionality, is evidenced by obtained values of the texture aspect ratio (Str) tending to 0.00 for all textured samples. Changes in the friction coefficient’s directionality in the forward and backward directions were noted for α values above 20° for both dry conditions and friction with lubrication conditions. We can conclude that laser surface texturing allows for the effective functionalization of a medical silicone surface in terms of the anisotropy of its tribological properties.