good day, is there a way to figure out the key a singer sings in a specific song by hearing? 

Great question! Many times, the last pitch of the melody will be the tonic (or the "home base" pitch), which is also the name of the key. If I sing "Happy birthday" and land on a C, I'm in the key of C. 

However, this isn't always the case! Ask yourself: which pitch would need to be sung or played for this song to feel absolutely complete, settled or resolved?

Another good check is: look up the chords on https://www.ultimate-guitar.com/ (the key is usually listed, though it can get a little confusing if it's usually played with a capo, since you may be playing chords in the key of G with capo 3, which will then put you in Bb). https://www.karaoke-version.com/ also has the keys of many popular songs listed!