Wikipedia says "The most famous musical setting of the poem was by Travis Edmonson of the folk duo Bud & Travis. Edmonson titled the song "Golden Apples of the Sun", and it was released on the 1960 Bud & Travis album Naturally: Folk Songs for the Present. Their version has been covered, sometimes as "Golden Apples of the Sun" and sometimes as "The Song of Wandering Aengus".

1962 Judy Collins recording, which she titles "Golden Apples of the Sun: https://www.youtube.com/watch?v=T48vA3BUYxI

Jean Redpath (1987): https://www.youtube.com/watch?v=M4GX9rf_CLE

Karan Casey (2006): https://www.youtube.com/watch?v=I7xhCuy-BTg

Here's a 1966 recording by Dave Van Ronk. I suppose it is the same melody Judy Collins used, but Van Ronk added his own affectation. I can't say that I like it.

https://www.youtube.com/watch?v=C4Zd5ilU2bU