The Elvish writing system used for the One Ring's inscription is Tengwar.
Tengwar is a writing system created by Tolkien for the languages of his legendarium. The word means “letters” or “characters” in Quenya. It was devised by the Elf Fëanor in the fictional history and later adapted for different languages and writing traditions.
The One Ring's inscription is written in Tengwar, but the words themselves are in the Black Speech of Mordor. This is one of the most common points of confusion in discussions of Tolkien's scripts: Tengwar identifies the writing system, not the language being spoken.
Another major Tolkien script is Cirth, a runic system associated especially with the Dwarves. Sarati is an older script developed by Rúmil, and Angerthas refers to expanded runic arrangements. These names are related to Tolkien's invented writing traditions but do not identify the script on the One Ring.