2 is grammatically correct.
1 is very common.
"I dropped the pen" avoids the issue.
Student or Learner
Which one is correct?
1. It was me who dropped the pen.
2. It was I who dropped the pen.
1 is very common, but I think that It was me that dropped the pen would be the most common, at least in informal British English.
You could also avoid the issue by saying I was the one who/that dropped the pen.
relating to this, I have another question,
1. It is them who are ill.
2. It is they who are ill.
It is they who are ill.