The approval for the denial of a credit card application has no direct impact on your credit score.
Whenever you make the application for a credit card the lenders requests a copy of your credit report from the credit bureau. This is shown as an enquiry which will be visible to the future lenders that you apply to for credit.
However it will not be showed as to whether the application was accepted denied. If the lender sees a subsequently opened new credit account then he may presume that the application was accepted. However, if there is no subsequent new account that it does not necessarily mean that the application was denied as many times the consumers shop around for the best deal and choose one only after having applied in more than one place. Since the approval or the denial of a credit card application is not shown to the lender it is not considered in the calculation of the credit score.
Sometimes consumers get pre-approved credit card offers in the mail as well. Not accepting these offers also does not have an impact on the credit score while it may mean that you are doing a good job of handling your credit since you are being targeted by credit card companies as a kind of consumer they want to have a customer.
You should be careful and exercise caution before accepting a credit card offer. Make sure that the credit card has the facilities that you want. Low interest rate may figure high on your list but it only counts if you were the kind of consumer that chases on the credit card and makes partial payment on it every month rather than paying off the full balance. If you do not revolver balance each month other factors such as annual fees, credit limit and incentives such as airline miles, cashback, 0% fuel surcharge and insurance might be more pertinent to your needs.
While the approval of the denial of an application for a credit card does not have a direct impact on the credit score making too many applications in a short amount of time may impact your credit score negatively even if for a short amount of time as it seems to the lenders and credit scoring models that you are trying to incur a lot of debt. Since it is unclear initially as to how you intend to manage this debt, creating instability in the financial reporting, the credit score may initially reduce.