It was rare as an American given name before 1975. In the mid-1980s it began growing in popularity for boys after a character by this name began appearing on the soap opera Ryan's Hope. It is now more common as a feminine name, probably due to the fame of the actress Dakota Fanning (1994-).
Because Elijah was a popular figure in medieval tales, and because his name was borne by a few early saints (who are usually known by the Latin form Elias), the name came into general use during the Middle Ages. In medieval England it was usually spelled Elis. It died out there by the 16th century, but it was revived by the Puritans in the form Elijah after the Protestant Reformation. The name became popular during the 1990s and 2000s, especially in America where it broke into the top ten in 2016.
After the Protestant Reformation it was occasionally used as a given name in the English-speaking world, and it became somewhat common in America due to the fame of the revolutionary Ethan Allen (1738-1789). It only became popular towards the end of the 20th century. It is the name of the main character in Edith Wharton's novel Ethan Frome (1911), about a man in love with his wife's cousin.