The writing system Tolkien used for many Elvish languages is called Tengwar.
Tengwar is a script created by Tolkien for the languages of Middle-earth. Its letters, or tengwar, represent sounds through a structured system of signs and tehtar, including vowel marks. Tolkien displayed it in texts such as the title page inscription of The Lord of the Rings and the Ring-inscription written in the Black Speech of Mordor.
Tengwar is a writing system, not a language. This distinction matters because Tolkien created several languages, including Quenya and Sindarin, which could be written with different scripts. Cirth is another Middle-earth writing system, associated especially with runic letters and the Dwarves. Sarati was an earlier script in Tolkien's invented history of writing.