Yes you can. You can pay your mortgage with a credit card in two ways.
The first way is to use the convenience checks that credit card companies send out every once in a while. These checks work the same way as checks you would write from a checking account, but they use your credit instead of the money in your account. These can be written, signed, and sent to mortgage companies by mail.
The second way is to pay your bills online (such as the type available at MBNA). This lets you send a certain amount to the company you choose. The amount will be taken from your available credit and given to the mortgage company in a way that is similar to writing a check.
What's wrong with these two approaches?
You won't get any cash back, miles, points, or other rewards for these purchases, which is the main reason to use a credit card in the first place.
So, is there any way to pay with a credit card and still get the bonuses?
There is, yes. There was, though.
There was once a time when you could use your credit card to buy Charter One gift cards. These worked the same way as ATM/debit cards and could hold up to $500 each.
Basically, all you had to do was buy these gift cards, take them to an ATM, pay the $3 withdrawal fee, and get $497 in cash while still getting your credit card bonuses. Then, you could put in enough cash to pay your mortgage and cover the payment with a check.
Getting cash from a credit card without paying huge cash-advance fees AND still getting your bonus rewards is a huge plus.
This programme was used in this way because it was easy to do, and when it became clear that it wasn't going to make much money, it was stopped.
But keep an eye out for more loopholes like this one, because they happen all the time.