in this sentence, isn't 'the singer' the subject?
and if it is, why does the subject take the accusative case?
"singer" in Turkish is şarkıcı, not şarkıç.
The -ı at the end is part of the suffix -ci, which basically means "person connected with ...". (It's -cı in this word because of vowel harmony. You might also see it as -cu or -cü.)
In this case, it's a person connected with songs (şarkı is a song) -- a singer.
Another useful -ci word is öğrenci "student", which comes from öğren·mek "to learn".
Long story short: şarkıcı is in the nominative case. (The accusative case form of that word would be şarkıcıyı.)