Peter, the C# is the third of an A7 chord. The F# (sometimes thought of as a sixth of the A major scale) is added to the 7th in the A7 chord to form a 13th. F# is the 13th of the A7 chord thus making a chord based on A7....an A13th.

Now you might ask the question, what's a thirteen doing in a folk song that only uses major, minors or sevenths? The answer is that the harmony is implied in the notes of the melody.

Frank