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.
As mentioned, copyright is automatic. The best form of defense is to only submit physical copies of your work until a publisher agrees to buy it from you to publish. This preserves the only digital copy on files you're able to access. Make sure you have a change log of your main digital copy, or attach to e-mails to yourself
An even dumber poor man's protection is to send yourself a self-addressed sealed envelope with a postmark (it doesn't hurt to send multiple of these, in case the package gets destroyed in one storage location or multiple cases occur). Wait until the next day and then send your manuscript to the publishers with postmarks. When you receive the sealed self-addressed envelope, do not open it, but store the unopened package in a place where you would secure files or if need be a safe deposit box. This will create an official government date (the postmark always contains the date it was recieved for delivery by the post office) and can be opened to reveal the manuscript at trial. Important to note is that these need to happen before you send your documents so you can show records that you possessed them prior to the publisher's records (the publisher would likely discard the envelop) and that there are two viable records of your prior ownership.
It's perfectly viable to only need one sealed envelop, as any records of proceedings where it was opened will suffice as evidence just as well as the initial record, since it acknowledges the initial record's existence. It's a poor man's copyright protection, but it shows original creation would belong to the person who has held the document the longest.