If you were to get a credit card right now, you'd have a hard inquiry on your report right away from the application. While the account many not report for several weeks or a month (or 2 months with some creditors like Amex) when the mortgage company does another HP they'll see that you applied for credit from the CC HP even though the account hasn't yet reported.
The scoring benefit you receive would happen after the account reports and you are then showing revolving credit usage, where you currently aren't. That's what I'm assuming anyway, that you have no current revolving credit lines, a question that CGID posed above.
I'm fairly certain the recommendation here would be to not apply for a card at this time. How are your credit scores? Are you already able to secure the best interest rates on a mortgage? If so, no need to take another HP right now. "If it ain't broke, don't fix it."
I would however strongly recommend taking on at least one, ideally 3 credit cards in the future though as they would certainly do great things for your credit profile.
