I've heard the word "singer" a lot but, does "song man" a common phrase?

Rebecca

No, the phrase "song man" is not a common phrase. In this sentence, "song man" is used to refer to both someone who writes songs, and someone who sings songs. However, it is not a general phrase that is used, and normally you can say "singer/songwriter" to express the meaning of one who writes and sings songs.