It's perfectly fine to pay off your credit cards in full but you should wait until the bill comes into the mail or you get billed online for the credit card before paying the bill.
Paying the full amount due on the credit card after you get the credit card bill will help improve your credit rating and credit score.
It's much better to pay the full balance off each month after using your credit card to help improve your credit score so it won't hurt your credit to pay the credit card bill in full.
What could hurt your credit score though is paying the credit card bill before you get the bill because then it could be reported as late even though you're paying it in full.
Wait until you get billed and then pay the credit card bill in full then it will improve your credit score.