Studies on the effect of wall textures and crystallographic grain orientations on graphene coatings and water droplets wettability are conducted. To date, there is almost no data on the effect of surface textures and high‐temperature annealing on the wettability of the graphene‐coated copper. It is generally accepted that the water contact angle on the graphene‐coated copper with one graphene layer is ≈85°–86°. However, changing the annealing duration, and using different surface textures, it is possible to change the graphene wettability over a wide range of static droplet contact angles from 81° to 96°, which allows providing both hydrophilic and hydrophobic properties. With the growth of annealing duration, the average grain size increases from 0.1–1 to 10 mm and more. By changing the annealing duration and the surface roughness, it is possible to realize the grains orientation (001) and (111), as well as the simultaneous presence of different grains orientations. Molecular dynamic modeling of the influence of orientation and grain size on the wettability of the graphene coating is performed. The calculation results correspond to the experimental data on contact angles. The key factors affecting the wettability of graphene are presented and analyzed.