The script J.R.R. Tolkien created for many Elvish languages is called Tengwar.
Tengwar is a writing system in Tolkien’s legendarium, whose name means “letters” or “characters” in Quenya. Tolkien designed it primarily for the Elf Fëanor, and it was used to write languages including Quenya and Sindarin. Its elegant letter forms are especially recognizable in modern presentations of Middle-earth.
Tengwar is not itself a language. That distinction is important: Quenya and Sindarin are languages, while Tengwar is a script used to represent them. Tolkien also developed different modes, or conventions, so the same script could represent different languages and sound systems.
Cirth is another Tolkien writing system, associated particularly with the Dwarves, while Sarati is an earlier script in the development of his invented writing systems. These names are therefore plausible alternatives but do not identify the script most associated with Elvish writing.