I dealt with something like this recently. In my case, the characters were listening to a record. I spliced in the appropriate portion of the song, and then it occurred to me that it might seem a bit jarring. I decided to use other parts of the song to create an intro and outro for the podfic. This made it all flow together better and sent a signal up front that There Be Music Here. In some cases that might be overkill -- I think it worked in this particular case because the story and song were really thematically entwined and shared the same name.

On the other hand, one of my future projects features a song that is sung by a character, and I'm planning to sing that one myself.