No you don't
From Massachusetts...
Myth: You need a photo ID to get SNAP/Food Stamps.
Fact: You need proof of identity. A photo ID is one way to prove identity. You can’t be turned down for SNAP/Food Stamps benefits because you don’t have photo ID. You can use another ID like a work or school badge, a health benefits card, an ID from another social service, a pay stub, a birth certificate, or a voter registration card. The SNAP/Food Stamps worker can also check your identity by calling shelter workers or employers.
From the GAO...
STATES MAY USE PHOTOGRAPHS ON
THE IDENTIFICATION CARDS BUT, UNDER DEPARTMENT OF AGRICULTURE
REGULATIONS, MAY NOT DENY OR DELAY BENEFITS TO HOUSEHOLDS
WHOSE MEMBERS ARE UNWILLING TO BE PHOTOGRAPHED.
From the USDA...
Identity
Driver’s License
Work or school identification card
Health benefits identification card
Voter registration card
Birth certificate
From lawhelp.org
You can't be denied for food stamps simply because you don't have a photo ID.
The Food Stamp caseworker is required to verify your identity. If you are unable to provide a photo ID, there are other ways to verify your identity such as wage stubs, a voter registration card, a birth certificate, or a "collateral contact" such as a homeless shelter case manager.