Since the election, fewer eligible San Franciscans are taking advantage of food stamp benefits because of fears about immigration crackdowns under the Trump administration, said Trent Rhorer, executive director of San Francisco’s Human Services Agency.

The city is concerned by a recent spike of withdrawals from CalFresh, or food stamps, among eligible households with at least one noncitizen. According to Rhorer, the political climate has sparked a rash of questions from participants, ranging from whether their personal information would be released to the federal government to whether the administration will cut food stamp benefits to immigrants.

The impact to those eligible families, and to the city, could be significant if trends continue.

“They are putting their household in further jeopardy of not being able to pay the rent, or not being able to pay utility bills because they have to buy food,” said Rhorer. “These are benefits they are entitled to receive, and they’re playing by the rules. They shouldn’t be penalized by this negative commentary coming out of the White House.”

California already has one of the lowest food stamp enrollment rates in the country. In San Francisco, about 52,000 people — only half of eligible residents — participate in CalFresh. That’s a similar participation rate to the state as a whole.

Legal residents, including green card holders and those with official asylum or refugee status, are eligible to participate in the Supplemental Nutrition Assistance Program (Snap), as the federally funded program is known nationally. In California, a family of four with a gross household income of less than $4,050 per month qualifies, and the average monthly benefit in San Francisco is $230. A household can qualify even if some members are not legal residents.

But since the election, statements from the Trump administration have raised concerns in immigrant communities about accepting food stamps. The agency identified a drop in new enrollments and a rise in withdrawals from the program, especially in the 9,500 participating San Francisco households with at least one noncitizen. In that group, 150 households withdrew from the program in March and April alone, whereas the normal rate is fewer than 60 withdrawals monthly. In the first four months of the year, new applications to the program have decreased by about 17 percent.

The numbers don’t yet constitute a trend, but it was enough to cause the city and other partners like the nonprofit SF-Marin Food Bank to hold a joint event Wednesday to encourage low-income residents to apply — and to address their concerns.

The draft of an executive order that was leaked in January, but never signed, was particularly worrying, according to Rhorer. Called “Protecting Taxpayer Resources by Ensuring Our Immigration Laws Promote Accountability and Responsibility,” the executive order called for a policy that would “deny admission of any alien who is likely to become a public charge” — such as immigrants who may require food stamps. It also called for identifying and removing undocumented immigrants who have received those benefits illegally.

Recent events have also raised concerns that accepting food stamps and other benefits could get in the way of obtaining a green card. According to the National Immigration Law Center, accepting those benefits can be a problem only for those who misrepresent their immigration status when applying.

“People keep asking, ‘How this might affect me?’ and ‘Do you know if there are any changes to the program?’” said Jaqueline Marcelos of the Mission Economic Development Agency, which helps residents apply for CalFresh.

Privacy is an ongoing concern. Families that qualify for CalFresh benefits because the children are citizens when the parents are not, for example, may choose not to participate for fear that their personal information will be released to the federal government. But the city of San Francisco, which administers benefits within the county, said information about household members who do not apply is not released to the federal government, which also doesn’t access its CalFresh systems for immigration enforcement action.

What’s unclear, however, is whether that policy would change if the executive order is signed. Also unclear is whether the administration will make changes to Snap that have been floated by House Republicans, such as adding new work requirements, which Agriculture Secretary Sonny Perdue has hinted are possible. However, Trump’s recently proposed budget cuts to the USDA did not include cuts to Snap.

This week, the Agricultural & Applied Economics Association made the case in a news release that the Snap program is “the central component of the social safety net against food insecurity,” said co-author Craig Gundersen of the University of Illinois.

In San Francisco, where 23 percent of residents struggle with hunger, the program has particular resonance. Many low-income families supplement CalFresh benefits with groceries from the food bank, said Paul Ash, executive director of the SF-Marin Food Bank, which distributes free groceries to low-income people. He said that without CalFresh, his organization would be overwhelmed.

“I just can’t stress enough how important having a strong CalFresh program is,” Ash said. “Some people think, let’s let private charities do it. But we can’t solve this problem.”

Tara Duggan is a San Francisco Chronicle staff writer. Email: tduggan@sfchronicle.com Twitter: @taraduggan