Is it possible for you see how many people viewed your answer?
Yes, it is!
You can see how many people have seen a specific answer by looking at that answer's impact map.
The impact map is located at the bottom of every answer page, in the bottom-right corner, right above the footer.
For example, visit this answer and scroll down to the bottom of the page.
SIDE NOTE I took that screenshot about
The impact map shows you exactly how many times a particular question, answered or unanswered, has been viewed.
Unanswered questions can have anywhere from a couple of views to a couple of dozen views, depending on how much time they spent on the site before getting answered.
After the question gets answered, the impact map will show all the views that the answer accumulates over time. Mind you, this number includes the number of views that the unanswered question accumulated before an answer got posted.