Well now you can. The details of the credit card contract are usually in small print on the back of the letter offering you the new card. Read it before you sign on the dotted line, and make sure you fully understand the terms of the credit card being offered. You might be surprised at what you find. But make sure the one you decide to take never has an annual fee.
Some cards are free only for the first year.
After that, you may be automatically billed for an annual fee. If the card you want has an annual fee or adds one after you've accepted it, ask the company to waive it. Some card companies will eliminate this charge to keep from losing you. Otherwise, shop around for a free card. There are plenty.