Hello there,
Yes, a MSW graduate can do PhD in psychology. With PhD, you can learn clinical skills and become a lisenced psychologist.
Some of the top colleges which offer PhD in Psychology are as follows :
1. Amity University, Lucknow
2. Allahabad University, Allahabad
3. Punjab University, Chandigarh
4. Banaras Hindu University, Varanasi
5. Kurukshetra University, Kurukshetra

These are some colleges where you can apply. If you don't get your required course in India, you can try abroad.

Hope this answer helps you.
Good luck!!