Yes, you can Apply. Master of Arts or M.A. Psychology is a postgraduate course in psychology which studies human behavior and human psychology. It is concerned with a thorough and comprehensive study of psychology as a discipline.
The duration of M.A. Psychology is 2 years and is spread over four semesters. Minimum eligibility for this course is graduation degree from any stream with min. 50% from any recognized university. However, there are some reputed institutes that allow entry to the students having an honors degree in psychology or has it as a subject in the graduation.
The average tuition fee of M.A. Psychology ranges from INR 2,000 to INR 20,000 for two years in Government funded colleges. For private institutes, tuition fee may be as high as INR 2 Lakhs. The most common route to this course goes through an entrance test. Most of the universities conduct their own entrance test.
Top Universities are:
Indian Institute of Psychology and Research, Bangalore
Annamalai University, Faculty of Science, Chennai, Tamil Nadu
Banaras Hindu University, Faculty of Science, Varanasi, Uttar Pradesh
Lovely Professional University, Faculty of Science, Phagwara, Punjab
Indira Gandhi National Open University, Faculty of Science, Delhi
Jamia Millia Islamia University, Faculty of Science, New Delhi
Jawaharlal Nehru University (JNU), Faculty of Science, New Delhi

Hi there.

After completing your BCom it would be a little tough to find college's for MA Psychology.

There are very few government colleges that have the provision of doing MA after BCom but in private universities and colleges you can easily into the MA Psychology course after graduating in Commerce.

1. Amity University, Noida - Among the private universities, Amity University of Noida campus has one of the best course structure of Masters in Psychology. You'll have to crack their interview round to get in.

2. Indian Institute of Psychology and Research, Bangalore - This again is a great Institute. The best part being it is only for Psychology. Imagine being around Psychology aspirants, great faculty, a beautiful campus and excellent facilities. This is the one of the places to be! (but, the amount of exposure here would be less than Amity)

3. Jain University, Bangalore - This is a world class University. With buzzing crowd of students, huge number of conferences and internships, the amount of exposure is limitless. This is a great option too!

4. Montfort College, Bangalore - You'll get all information regarding this on Google. I'm mentioning it here becsuse it is one of the colleges that will provide MA after BCom.

Among Government Universities, Delhi University is the one that provides MA after BCom.

Again, getting into Delhi University for MA Psychology is very difficult.

In North Campus, they have the course on MA/MSc in General Psychology with somewhere around 100 seats. In South Campus, the course is on MA/MSc Applied Psychology with around 30 states. Both have different entrance examinations, after clearing which you'll have to appear for an interview to get selected.

Next, in your case, you can check Jamia Millia Islamia, that too provides MA after unrelated subject graduation and Banaras Hindu University does the same too.

Hope you find this helpful.

Good luck!