Fran D'Alcorn, of the independent St Felix School, in Southwold, Suffolk, suggested the sector as a whole could provide places for a thousand children.
The UK will accept up to 20,000 Syrian refugees over the next five years.
And Miss D'Alcorn said the orphans among them would put pressure on local authorities, children's homes and fostering services.
Boarding schools could offer them pastoral support as well as a good education, she said.
In World War One, St Felix had helped children from Serbia, she said. In the 1930s, it had taken in refugees from the Kindertransport, which brought children from Nazi Germany. And in the late 1970s, the school had taken in children of the so-called Vietnamese boat people.
Boarding Schools' Association national director Robin Fletcher said: "We know educating the next generation is key to the future success of any country, not least a war-torn country such as Syria.
"Our boarding communities can provide a safe haven in which the refugees can have access to a strong network of pastoral support and structure including counsellors while continuing their education."
A boarding school head offering two free places to orphaned Syrian refugees is urging others to do the same.