Career switch from B.Tech to Psychology

Yes. You can do an MA or MSc in Psychology without having graduation in Psychology. The eligibility criteria will vary from university to university. MA Psychology is offered by many top universities for graduates with 50% marks in their graduation. So if you got more than 50% in your B.Tech you can apply for that.
Admission to the course in some colleges based on the marks they obtained in the degree and some colleges based on the rank obtained in the entrance test. Some colleges will conduct oral test also in addition to the written test. Almost all major universities are having this course and you can go through the website of the university and decide.
There are some universities which are offering distance mode or private mode also. IGNOU is one such university.
Once you get admitted into this course you can opt for any specialisation you like. There is no restriction as such.
The following are some of the institutions offering this
1. Hindu College, New Delhi.
2.Ferguson College, Pune
3. St. Xavier's College, Mumbai.
4. Symbiosis college, Pune
5. Mithibai College, Mumbai.

You can persue post graduation course in Psycology from some recognised university though you might not have opted Psycology as one of the subjects in your graduation stage.
Since you are a B.Tech in CSE, your possibility of admission to M. A. In Psychology would depend upon two factors -
1) In no case, your aggregate marks is not less than 50 percent of your qualifying examination provided no restriction is imposed by the university authority regarding Psycology being one of papers at graduation - stage.
2) If there is the entrance test if any for the selection of aspirants, you will have to clear the same including the viva of the selection- committee.
Once you have cleared the selection criteria, you will be taught different subjects of Psycology such as Clinical Psychology, Organisational Psycology and other areas of Psycology included in the courses of studies.
There are different universities which can be chosen for their better reputations and choose anyone of the following -
1) Presidency College, Kolkata
2) Ferguson College, Pune,
3) Symbosis College, Pune
4) Indira Gandhi National University
5) Himachal University, Shimla
6) Punjab Univesity
In case, you feel time constraints due to your other assignments, you can take up the post graduation courses through IGNOU from where you will get the entire course material apart from the guidance of the expert - faculties removing your doubts in course of studies through the doubt removing session arranged in their programme.

If you have a keen interest and liking for Psychology you can definitely acquire the PG degree in it after the engineering degree. The eligibility criteria is varied and mixed one across the different colleges but many colleges do not insist for a graduation in Psychology subject for admission to MA in Psychology. In that case you can very well apply in them. In general the eligibility criterion will be some or all out of the following requirements -
1. Any graduate degree.
2. Minimum 50% marks in graduate degree.
3. Psychology as one of the subjects during graduation.

As regards the admission it also varies and some colleges just take on the basis of merit based on marks of graduation while others take based on their own entrance examinations. One has to check this aspect in the University/College website.

Some of the institutes take entrance test where questions related to Psychology are asked. Some of such institutes are as follows -
1. Tata Institute of Social Sciences.
2. Banaras Hindu University.
3. Jammu University.
4. Delhi University.
5. Osmania University.
6. Fergusson College, Pune.
7. Hindu College, New Delhi (Note: It takes student in both the modes).

Some of the colleges which simply follow the merit criterion and do not conduct entrance test are -
1. Mithibai College of Arts, Mumbai.
2. IGNOU.
3. Banasthali University, Jaipur.
4. Hindu College, New Delhi (Note: It takes student in both the modes).
5. St. Xavier's College, Mumbai.
6. Symbiosis College of Arts and Commerce, Pune.

Other than the above there are some more universities/colleges where one can apply after finding the mode of admission by going to their websites. These are -
1. Lady Shri Ram College for Women, Delhi.
2. Deen Dayal Upadhay, Delhi.
3. Calcutta University, Kolkata.
4. Panjab University, Chandigarh.

You can apply for a postgraduate degree in psychology from any college, for this it is not necessary to have a psychology subject in the graduate, based on the information you are looking for, suggesting some names of the college whose details are also available on the internet. -

West Bengal has the following colleges for postgraduate in psychology -
LC- Loreto College
University of Calcutta

Vivekananda College for Women
University of Calcutta

KDDC-KD Degree College
Bhupendra Narayan Mandal University
Raniganj, India

SC-Salesian College
calcutta university
Siliguri, India

TDBC-Triveni Devi Bhalotia College
University of Burdwan
Raniganj, India

BRSC-Barrackpore Rastraguru Surendranath College
University of Calcutta
Parganas, India

GFGC-Government First Grade College Krishnaraj Nagar
University of Mysore
Krishna Nagar, India

WCC-Womens Christian College
University of Madras
Kolkata, India

VI-Victoria Institution
University of Calcutta
Kolkata, India

JDC-Jogamaya Devi College
University of Calcutta
Kolkata, India

AC-Asutosh College
University of Calcutta
Kolkata, India

GGDC-Government General Degree College Hooghly
University of Burdwan
Hooghly, India

GGDC-Government General Degree College Singur
University of Burdwan
Singur, India

CU-Calcutta University-

MKC-Maharani Kasiswari College
University of Calcutta
Kolkata, India

Apart from these, some good institutes of Psychology in India for studying at undergraduate and postgraduate level are as follows:

University of Delhi, Delhi,
www.du.ac.in,
Jamia Milia Islamia, Delhi,
www.jmi.ac.in,
Punjab University, Chandigarh,
www.puchd.ac.in,
Christ University, Bangalore,
www.christuniversity.in

If you want to pursue postgraduate in psychology subject definitely, you are eligible to apply. As mentioned above, You are a B.tech student but there would not be any problem in pursuing this course. For pursuing this course, psychology subject is not necessary on the graduate level. Student who belongs to different discipline can apply for this course. You should have any graduate degree with 50% marks. For getting admission in these courses, the procedure varies from University to University. Some university takes admission on the basis of graduation marks. Whereas, some university conduct entrance exam where you will have to qualify for getting admission.
There are some colleges for postgraduate courses in west Bengal as follow:-
1. Vivekananda college
2. Women Christian college
3. Calcutta University.
Apart from this, there are some reputed institute in India which provide quality education as follows:-
1.punjab University, Chandigarh
2.Hindu College, New Delhi
3. Lady Shri Ram College, Delhi.
4. St.xavier's college, Mumbai.

Many colleges give admissions to graduates of any discipline for their MA Psychology courses. Some institutes insist for having Psychology as a subject in the graduation. So one has to find it from the college or university site one is sorting for the purpose. Some of the colleges in West Bengal where one can apply for MA Psychology admission, without having Psychology as a subject in graduation, are -
1. Bethune College, Kolkata.
2. University of Burdwan, Bardhman (WB).