This question is asked time and time again by so many music students.
Every year thousands of courses and lessons are taken by people who desperately want to sing on-key or be able to play any song by ear on their instrument.
It's definitely a coveted trait to have in the music industry and hopefuls know this.
But, sadly a lot of of those hopefuls don't have it and, what's more, they don't think they can learn it.
Well, they're wrong.
So, the answer to your question, "Can I learn perfect pitch?" is "Yes, you can!", and here's some things to consider...

•  You already possess relative pitch! -  We have a uniqueness as humans.
   We all are blessed with the skill to pick out pitches in regard to their affiliation to other pitches, a capability labeled relative pitch.
   Studies show that animals do not have this capacity.
  Take a recent study on birds, for example.
  Scientists found that birds can easily recognize an arrangement of repeated notes;however, when the particular order of those notes is transposed even a little bit, the bird doesn't recognize it.
  So you're one step ahead just by being human!
• You could already possess absolute pitch! - Scientists have discovered that many more people may have absolute pitch (the ability to recognize and name any note or chord by ear) than previously thought.
  All the earlier tests done were made for people who already had musical training.
  A new test has been created based on the way a baby recognizes words.
  This allows people of all kinds to be tested (whether or not they've had musical training).
  The research showed that there were a great many "non-musical" individuals who had absolute pitch!
• People of all ages, races and backgrounds are learning it! - This is the best observation.
  There are many programs out there that have taught and are now teaching individuals to sing on-key or play on their instrument any song they choose from memory!

So, we've answered the question, "Can I learn perfect pitch"? But, what about those who know they don't have it?