No, your debit card won't help you build credit

Your credit score is a reflection of your CREDIT history. Remember: your debit card is basically cash. It doesn’t count towards your credit history. Therefore, if you use your debit card to pay for things, then you’re not building your credit.

If you want to improve your credit score, then you need to use your credit card (and pay it off on time). Even if you select “credit” at checkout, your debit card is still a debit card, and it doesn’t change your credit score.