How can I delete the birth year on my IMDB page?

Go to the page about you (note that it's a page about you, not your page) and click on the Edit Page button near the bottom of the page.
Select Date of Birth ... Correct / Delete
Hit Continue
Set Action = Correct
GIve your correct date of birth
Optionally, you can also give/correct the place of birth
Give an Explanation in the form of a URL giving proof of your correct date of birth
Hit Check these updates
The backgound should turn green(ish) and it should offer you a Submit button
Hit the Submit button to submit your request

Sit back and wait for it to be checked, approved and implemented

    Steve