The correct answer is: Do you have any pens?
This is because “any” is used as a determiner for plural countable nouns when we do not know the specific number of them. It is also used for uncountable nouns. In this case, the noun, pen, is countable. So we can only use any for the plural form of pen, pens.
If we were asking for a single pen, we would use the article “a”, as the determiner. This is used for singular countable nouns. Then the sentence would be:
Do you have a pen?
The difference in meaning between the two is:
Do you have a pen? – Do you have a single pen?
Do you have any pens? – Do you have one or more pens?
