When you perform a song that was already released by another artist, you cover the song. This is usually only used when performing or recording it though.
You could also say rip off, but this is usually derogatory - you may "rip off" a riff or a chord sequence from another artist, meaning you copied it without permission (this can get you in a lot of trouble though!)
As Chevere33 pointed out, to rip a song is to upload it to your computer from a CD.
To rip off a song is to write a song extremely similar to the original.
As to your actual question, I can't think of a better way to say it than "to learn the chords of a song". You could say, since you are listening to the song not looking at a chord book, "to figure out the chords of a song".