You have to complete you graduation or should be appearing for your final year exams at the time ofcat filling the application form. Now there are 2 things about pursuing your Masters in Psychology.  Either you have Psychology as a subject in your Bachelor's degree or you don't. Few Universities need to have a mandate Psychology subject in your Bachelor's degree. However for few universities, Psychology is not a mandate subject. I pursued my Masters in Psychology from Acharya Nagarjuna University and they required Psychology as one of the subjects in Bachelor's degree. Based upon the choice of your University and whether you have studied Psychology or not, choose the University.

Below is the list of the universities that offer MA in Psychology:

Acharya Nagarjuna University

Andhra University

IGNOU

Barkatullah University

Karnataka State Open University

Nalanda Open University

Osmania University

Uttaranchal Open University

University of Mumbai.

Hope this helps!