Certainly. All over the internet, on posters all over the department walls, there are sites and numbers where you can report suspected food stamp/card/coupon fraud.
For starters, try 1-800-479-6151.
There should be provisions for you to remain anonymous (at least to the client)when reporting to one of these numbers. Information about "Who turned me in?" is not something they commonly provide the client being investigated.
What this will do is trigger an investigation of this person's case. The department is required by law to investigate a certain number of cases a year.
What they do to begin to comply with this requirement is to investigate people who have been reported for fraud. If the person is doing nothing wrong, there is nothing they have to worry about, and they are thoroughly informed each time they certify that the department has the right to subject them to extra scrutiny, even if they are never reported for anything. So they may not even know they have been reported, though they may suspect it.
The one thing they will NOT do is tell you what happened as a result of your report. If you hear later that the person lost eligibility for food assistance, you may suspect you brought this about. But you'll never have any ownership of the situation, in other words, you'll never know if your report resulted in an actual discovery of fraud. Sometimes it is tough to prove fraud, but if the person is investigated, it tends to sharply curtail their enthusiasm for continued misuse of the program. This may be as good as it will get. You won't be told, either way.
Reporting someone you're angry with for program fraud is very common. It's one of the reasons I always used to encourage my clients to stay very honest, because someone will always be willing to tell on you, and you will get caught eventually if you break the rules.