Do you need a credit card to sign up for psn?

No you don't need it. That is the normal way to add money to your account or you can purchase the PlayStation network card and this is quoted about the card from related link:

"The PlayStation®Network Card (PSN Card) is a prepaid card that may be used to apply funds to a PlayStation®Wallet without using a credit card. Please visit your local authorized PlayStation®retailer to purchase the PSN Card."