Both are correct.

Hi Ivan, my English is based on what I hear and use, so, 'I have a pen', sounds right to me because, that is what I would use. Cheers...

Have you got a pen.? Is more immediate . I have a pen could mean you own a pen but it is at home. I have got a pen suggests you could pull it out of your pocket and lend it to me right now.

You would hear both in conversational, informal speech, and in informal or colloquial written English, but it would be considered sloppy to include the 'got' in formal written English. Personally I always omit the 'got' even in casual informal conversation...but then I'm a little pedantic! How many pens do you have? (grammatically correct) How many pens have you got? (colloquia and very commonl) I have three... (grammatically correct) I've got three... (colloquial and very common...)

I have a pen. "I have got a pen." would be incorrect English.