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.