Short answer: no.
Only the following categories of foreigners are eligible to apply for permanent residence:
- Spouse and unmarried children (below 21 years old) of a Singapore Citizen (SC) or Singapore Permanent Resident (SPR)
- Aged Parents of a SC
- Employment Pass/ S Pass holders
Hence, unless you are under the age of 21 years old with Singaporean / PR parents, or married to a Singaporean / PR, you will have to wait till you join the Singapore work force before you can apply for PR on your own merits (expertise, skills sets, knowledge, experience and performance in your professional aspect, etc).
Being a PhD may give you an advantage in your PR application in terms of your academic aspects, but there are many other factors that affect your PR which the Singapore government will take into consideration (what the population demographics require, existing industry requirements, your skill sets, etc.)
Then what really sets a good candidate apart is the completeness of documents, good supporting documents (such as testimonials) and a solid commitment to Singapore (proven through social integration efforts).