Should I copyright my material before sending to my publisher? Can they steal my content?
Technically, your question is meaningless. By law, everything you write is copyrighted the instant you write it. You can REGISTER your copyright with the Library of Congress. This registration can be used as evidence that you did indeed write it, and gives you certain additional legal rights.
But more to the point, the answer is no, don't register the copyright before sending to a publisher. This jumps the gun in a number of ways. Almost every publisher will want to make editorial changes to your work, so a new copyright on the updated work would have to be registered anyway. And getting published means that you are selling certain rights. Part of the deal may be that you are selling all your rights. (Which you may be willing to agree to or not.) So any registration may have to be amended.
And even more to the point, publishers are not in the business of stealing the work of aspiring writers. As @cloudchaser says, if a publisher did this regularly the word would surely get out soon enough, and then no one would want to send them any submissions and they'd be ruined.
New writers are always asking, "how can I protect myself from my work being stolen?" Seriously, just don't worry about it. As a new writer, your problem is to get people to think that your work is valuable. Spend your efforts trying to write something good enough that someone would want to steal it.
(I once found that one of those services that sell pre-written term papers to cheating college students was selling an article that I wrote without my permission. My first thought was that it was great that people were actually willing to pay for copies of my article. I never bothered to do anything about it.)
They can, but they won't.
A publisher who steals submissions will soon be out of work, because no one will want to work with them.
Also, once your text has gone through your beta readers you will have enough witnesses and several versions of your text, and proving that you have written it will be totally easy.