If I take the standard deduction and don't itemize can I still take a portion of the mortgage interest for my home office?

Yes.

Yes, you can still use the mortgage interest for your home office.

To enter your home office expense along with other common business expenses:

1. Open or continue your return.
2. Search for Schedule C and select the Jump to link in the search results.
3. Answer any questions about your business until you get to the Your self-employed work summary screen. Select Edit or Review next to your business.
   • You might want to enter your 1099-MISC, 1099-K, cash, and personal check income from your self-employment before you associate any expenses with your business, but this is not required.
4. You'll be asked What kind of expenses did you have for [type of work]? Select Home office. You can also select any other expense categories that apply to your business. Select Continue at the bottom of the screen when you're done.
5. On the Here's your [type of work] info screen, scroll down to the Expenses section, and select Start  next to Home office.
6. Enter the info about your home office.