Yes, asking for a lower interest rate on a credit card could affect your credit score if the card's issuer needs to do a hard inquiry into your credit history to determine whether or not you qualify for the lower rate.
A hard inquiry will typically drop your credit score by a few points, and it can only affect your score for up to 12 months. So, the potential negative impact is minimal. That said, receiving a lower interest rate may indirectly help raise your credit score if the new rate allows you to pay off your balance faster.
It's worth noting that interest rates aren't reported to credit bureaus and have no direct impact on your credit score. A hard inquiry is the only reason your credit score would drop after requesting a lower rate, and asking your card issuer for a lower rate won't always trigger a hard inquiry. A hard inquiry only happens if they need more detailed information about your credit history to address your request. Card issuers seem to make this decision on a case-by-case basis.
If you are thinking about calling your card issuer to ask for a lower interest rate, and you're concerned about the impact to your credit score, make sure to ask the rep about it along with your request.