Yes, you can borrow funds to use as your down payment. However, any loan you take out for a down payment must be secured by an asset that you own. If you own something of value that you could borrow funds against such as a car or another home, it is a perfectly acceptable source of funds. If you are planning on obtaining a loan, make sure to include the details of this loan in the Expenses section of the application.
For a more detailed explanation on the guidelines please check out the HUD Borrowing Guidelines.