There are multiple acceptable variations.

May I borrow your pen? (polite request)

Will it be OK if I borrow your pen? (type 1 conditional - not polite enough for most situations)

Would it be OK if I borrow your pen? (mixed conditional - conditional "would" of politeness)

Would it be OK if I borrowed your pen? (type 2 conditional of politeness - not a true type 2 for an unreal situation)

More examples:

Will your brother Joe be upset if I borrow his bicycle without permission? (type 1 conditional - real situation - I am thinking about taking his bicycle)

Would your brother Joe be upset if I borrowed his bicycle without permission? (type 2 conditional - unreal situation - I am not thinking about taking his bicycle)

Would your brother Joe have been upset if I had borrowed his bicycle without permission yesterday? (type 3 conditional - unreal past situation)

minor correction - Why DO we use "borrowed" ...

This is a type 2 conditional.

Actually it should be borrow. For instance can I borrow your pen. Do you mind if I borrow your pen. Borrowed is past tense

Oh, thanks Chris, you're right