In recent years, ocean current turbines have proven to be a reliable device for renewable energy generation. A crucial element of these turbines are the foundations, since they limit the displacement of the turbine, which is key in achieving efficiency in energy conversion, and can account for up to 26% of the total cost of the project. Most design procedures for foundations focus on sandy and clayey soils, but rock soils often predominate in tropical locations where marine currents are suitable for the installation of this type of turbine. This paper presents a design procedure for steel pile anchors (PAs) and concrete dead weight anchors (DWAs) on weak rock soils, using the assumptions of current technical documents and design codes commonly used in the industry for marine structures. Using specific designs for PA and DWA anchors, the procedure was theoretically assessed for a site off Cozumel Island, Mexico. The results show that the dimensions needed for DWAs are substantially larger than those for PAs. Therefore, whenever drilling is economically and operatively possible, piles would be preferable for the foundations of current turbine systems.