There are many pros and cons about nepotism in organizations, but your question seems to ask whether it is legal, not whether it is a good idea.  Although many object to the concept, nepotism is generally legal.

That may not be a full answer to your question, however.  This is another situation where, if you don’t know what legal box you are in, you don’t know what rules apply.  If your nonprofit has a tax status other than that as a private foundation and you can engineer the employment, you should be on the right side of the law, as long as the compensation is reasonable if you are a 501(c)(3) public charity or a 501(c)(4) social welfare organization.

If your nonprofit is a private foundation, however, you are probably a disqualified person with respect to the foundation by virtue of being a substantial contributor or a foundation manager.  If so, your son is by definition also a disqualified person.  Even that doesn’t mean you can’t hire him to work for the foundation, but you can hire him only for reasonable compensation and only to provide services necessary to carry out the charitable purpose of the foundation.  You can’t hire him for peripherical work, like cutting the grass outside the office building or performing other janitorial services.  If you don’t hire him for work necessary to carry out the charitable purpose of the foundation, you will have an act of self-dealing that could be very expensive for you and your son.  (See Ready Reference Page: “Private Foundations Must Avoid Self-Dealing”)