Is it correct to say:
"Did I tell you about the time when I ran over a chicken?"
Yes, Ashraful, it is correct to say that, assuming a time period for the past tense is understood. Otherwise "Have I told you . . . ?" would be better.
If it's correct can I say:
"Did I ever tell you about the time..."
Yes, you can.
What does 'ever' add here?
It emphasizes "at any time" during the time period under discussion.