Anybody can learn perfect pitch and some answers here are off-track.
Their is a secret to perfect pitch and it is very simple. Learn th recognize the A-440 pitch on a piano, which is middle A note.
Once you memorize that sound, then you can use it as a starting point and try singing one tone higher and compate this with the B sound on the piano. Or , go down and compare with the G note. etc...
Also, anybody who can sing on key has a form of perfect pitch. Otherwise, he or she would sing off-key correct ????
Another secret is to listen and play with a lot of music to develop ear-training. Once you have a good ear, you will be able to pick up keys of a song without touching your instrument.
Lastly, perfect pitch has NOTHING to go as to the quality of the musician. NADA. Some musicans go deaf and they play by memory knowing exactly what each note sound like and without making a mistake.
Berklee Graduate / Luthier / Studio Guitarist