The writing system used for the Ring inscription in The Lord of the Rings is Tengwar.
Tengwar is a script created by Tolkien for the languages of Middle-earth. In the story, the One Ring’s inscription is written in Tengwar letters, although the language of the words is the Black Speech of Mordor. The script’s elegant appearance has made it one of Tolkien’s most recognizable invented writing systems.
Tolkien described Tengwar as having been devised by the Elf Fëanor in the First Age. It was adapted to represent different languages, so the same script could be used for languages with different sounds. This is why identifying the script and identifying the language are separate tasks.
Cirth is another Middle-earth writing system, associated especially with angular runes. Sarati is an older script created by Tolkien for his mythology. These names can appear together in reference works, but they do not replace Tengwar as the script used for the Ring’s inscription.