Question: Is it safe to apply for a credit card
Answer: Most online application sites include encryption which is a tad too complicated for this answer, but it does offer stringent security. Therefore, filing an application online is as safe (if not safer) as charging to your card online. Can a hacker get in? I suppose, but chances are unlikely as most sites are protected from such activities. It is impossible to say fraud does not occur, but it is more likely to occur from someone opening your mail box or sifting through your garbage or copying your credit card number while your card is out of your sight in a restaurant.
Secure e-commerce technology is actually considered safer than mailing your paper application through the United States Postal Service. Of course the safest technology is filling out an application in person at the financial institution. But short of that, an online credit card application is probably a safer route than mailing.