Here’s the exact language:

Can I use a prepaid card or gift card?

We allow credit, debit and prepaid, network branded (e.g. American Express, Discover, MasterCard, Visa) cards registered under your name to be added to Venmo. Cards may be declined by the card issuer or Venmo for funds availability or fraud prevention reasons. Also, some payment cards may require a zip code to be linked to your account.