Yes you can! If he has provided consulting services to your self-employed business or corporation and he has been paid over $600 for the year. Of course, your Dad should not be a corporation.
There is nothing in the tax code that prohibits a relative from not qualifying to receive a 1099-Misc. But, he cannot be an employee, which would require a W-2, but rather he should be a professional such as a CPA, Lawyer or an IT consultant providing services as an independent contractor or consultant.