Consumers are often worried about applying for new credit cards because they don't want to get denied and hurt their credit scores. While no one likes to get rejected, the truth is the rejection itself actually doesn't hurt your credit scores.
The small hit your scores will take, usually around 5 points or less, occurs when you apply for the credit card and your credit history is pulled by the credit issuer. Whether your application is accepted or denied will have no immediate bearing on your scores.
Of course, the less hits on your credit reports, the better for your credit scores. So carefully do your research first and make sure the credit card you decide to apply for is a good fit for your credit profile.