Yes, even superhero’s have birthdays even the ones who weren’t born on Earth. Superman was born on Krypton on a day that correlates to the Earth date of February 29th, 1938.

As revealed in the pages of DC’s 1966 World's Finest Comics #164,

So, while Kal-El was born on Krypton on this date, that means he arrived on Earth sometime after that. This was also addressed in a later publication, that Clark Kent’s birthday is on June 18th. Which is the day that Jonathan and Martha Kent set as Clark’s birthday as it was the day that they found Kal-El’s crashed Kryptonian spaceship.

Happy 86th Birthday Kal-El! You don’t look a day over 30.