Pay Using Venmo On Mobile Devices
According the Venmo help page, on mobile devices only, you can opt in to pay using Venmo on this website.
How to set it up: In the Venmo app, tap the menu icon (three lines) in the top right. From there, tap on Settings. In settings, you should see a Buying Option, Connect Browsers, or Enable Mobile Web Purchase. Click on it and follow the prompts to connect your web browser.
After set up: When you check out, tap PayPal and you will be given the choice of paying with your PayPal or Venmo account.