The answer to this question depends on four factors. If you are opening your first credit card, a new card account could improve your credit score. Without a credit card it is possible that you do not even possess a credit score. After six months of this new account, enough information will exist for the credit score calculation to create a score for you.
For other scenarios, opening a new card can hurt your score some. It creates a hard inquiry that shows up on your credit report when you apply. This remains whether or not you accept the card or receive approval for it.
Since these types of inquiries are a 10 percent component of your credit score, every subsequent hard inquiry could mean the loss of several points on your credit score. This could be the difference between a good and bad credit score (translating to a good interest rate and a mediocre one on a loan).
Another factor with a new card is that new credit cards reduce the age of your average credit. Another 15 percent of your score component comes from the age of your credit (measuring your experience in managing credit). All else being equal the greater your credit experience, the higher your score will be.
Two elements make up your credit age component. It measures the age of your original account as well as your average length of history for all accounts. The longer it has been since you opened your last account, the more this will reduce the average age for your credit accounts.
The last factor has to do with credit utilization, which makes up 30 percent of your credit score. If you do not make major purchases on your new credit card, then your credit utilization ratio will drop and so improve your score. Should you open a new account and immediately run up the balance, then your credit utilization may increase enough to cause a substantial hit.
You should seek to keep this credit utilization number below 30 percent (and even better under 10 percent) as much as possible. The more of your new credit limit you are utilizing, the worse the impact on your credit score will be.