Yeah! You can definitely for the Assistant Professorship, if you have done MA in Psychology by qualifying the required examination in your state through which recruitment of professors are done.

Now in general, now-a-days, having a PhD degree/NET qualified in the subject, is a requirement asked by many institutes. So if you can qualify the NET or if you are interested to go for research, then after the completion of PhD go for it, and it will be a better choice, in terms of promotions and getting selected.

For more information regarding Psychology as a career consider the link below:

https://www.careers360.com/courses/psychology-course

For more information regarding NET consider the link below:

https://competition.careers360.com/exams/ugc-net

I hope this helps. Wish you a great eve!