We don't tend to congratulate people on simply having a birthday. Everyone has one, once a year. It's not an achievement. We congratulate people on passing an exam, passing their driving test, getting married, having a baby and similar life events.
Are you aware that "call on me" means "come to my house"? Did the person visit you at home or phone you? If they phoned you, you need "call me". I'd probably say "Thanks for ringing to wish me 'Happy birthday'!"
Student or Learner