Can I use Venmo as a payment method for my nonprofit?

Short answer: They don't officially support it yet.

Venmo is not available to nonprofits. The platform is not able to issue tax-compliant receipts and therefore the platform is not a viable option for online giving. 

Venmo's website explicitly states: Venmo’s peer-to-peer experience cannot be used to solicit or collect charitable contributions

Donations made via Venmo would not provide the name or email address without adding additional steps fo the donor to complete, which eliminates the convenience factor of Venmo.
Fundraise Up does not currently have plans to integrate with Venmo. If Venmo does eventually choose to officially support nonprofits, we will look into those integration possibilities.
Venmo is not usually available on large nonprofit websites as a payment method. Some smaller platforms will offer Venmo, but not as an officially supported method (meaning if there is a problem, Venmo will not support it).
To avoid these kinds of issues, Fundraise Up avoids payment methods that aren’t officially supported. Providing a Venmo workaround would leave nonprofits exposed to risk.