No. That is a misunderstanding of copyright law. One does not apply for a copyright. One registers their copyright with the US Copyright office (or the copyright office in your country). That simply gives the government a record of your claim to copyright on a particular work, especially if it is to be published in some format.
If you have a registered copyright with the government, and someone wishes to claim that they hold that copyright, they have the burdon of proof in court of law to prove you are not the copyright holder.
Likewise if you are wishing to challenge someone's misuse of your works, you have the upper hand in a court of law.