In an honest-to-God oral tradition "folk" song, it is, as pointed out above, not only permissible but nearly compulsory.

If it's a song of known authorship, and the author is dead, and the song's gone into public domain, probably no one's going to complain.

If the song is of known authorship, and still under copyright, you'd better get permission from the author and/or copyright owner.

One of the things that bug me about "Rise Up Singing" is their love of changing lyrics to make them more politically correct, without worrying about permission.

Peter