A credit card rejection has no effect on your credit score. When you apply for credit the issuer checks your credit report and score. This is called an inquiry. An inquiry will temporarily lower your score by a small amount. If your application is approved, a new account will be reported to the credit bureaus. This may lower or raise your score, depending on your specific circumstances. If the application is not approved, nothing is reported, and your score is unchanged.
I have never thought this to be the case. I think a credit pull and rejection counts the same as an approval and with no new credit line, actually hurts your score.