Can I apply for MS in software engineering in USA from a non CSE background? Can I apply for MS in software engineering in USA from a non CSE background? If so, then which universities generally accept with such condition? And how can I make my chances better?
First, let me say that from my point of view, I see masters' programs as broadly divided into two categories:

The first one contains courses that combine students from two different backgrounds, e.g. biology and IT (bioinformatics), law and IT, finance and IT, etc. In these courses, more introductory modules will be offered, e.g. data structures, programming etc. that are elementary for people with a background in IT but challenging for the others.

The second one contains "advanced" courses, that is people wanting to further specialize on the degree they have obtained. E.g. an "advanced computer science" master will not cover elementary issues (such as databases or computer architecture) but will have more cutting-edge, more advanced topics, closer to concurrent research.

I believe your best bet would be to apply for a master in the first category. I would look for something like "IT for architects", and not for courses with "advanced" in the title.