Can a landlord in the U.S. offer a special deal to move in tenants who, let's say, have Ph.D.s or Master's degrees? Is this legal?
Education level is not an FHA protected category. However, whenever you give one broad group preferential treatment over another, you'll raise eyebrows. Someone might argue, for example, that while your incentive does not explicitly mention a protected category like race or sex, it might disproportionately impact one group in a protected category over another.
In fact, the Supreme Court in 2015 addressed this question in Texas Department of Housing and Community Affairs v. Inclusive Communities Project. They found (albeit by a 5-4 vote) that disparate impact could, under certain circumstances, be the basis for a discrimination claim under FHA. The Wikipedia article on this subject is informative.
As for your case, it really depends on what you are trying to accomplish with the policy, and what you reasonably predict it will do. For example, given that in most areas, white people more often have graduate degrees than black people, then if this policy did in fact end up advantaging white tenant over black tenants, someone might claim that you are in effect discriminating on the basis of race. I would not want to be on the defending end of that claim.
In general, if you want to be safe from FHA's wrath, you need to evaluate each applicant on their individual merits as a tenant, not their membership in some group. Whenever you treat one person differently from another person, you should have a reason that clearly derives from your business interests as a landlord, and you should write it down.
Legal questions aside, it seems like a really bad idea to offer incentives like this. I can't imagine it achieving any legitimate business goal, and I can easily imagine it making tenants or applicants feel cheated and devalued. And when people feel cheated and devalued, even if they haven't legally been wronged, they often seek legal redress. Or slash your tires.
The fact that grad degrees would not be required under your policy isn't relevant. In the eyes of the FHA, any disparate treatment on the basis of a protected category is discrimination. The only real question here is whether this is disparate treatment on the basis of a protected category.