The D.C. City Council voted yesterday to consider restoring $13 million cut by Mayor Marion Barry from next year's city school budget.

Council Chairman Arrington Dixon said the money could be provided by reducing all noneducational spending in the proposed $1.5-billion budget by 1 percent.

The school budget for the current 1980 fiscal year is $250 million. Barry, citing reduced enrollment, has proposed an outlay of $237 million for fiscal 1981, rejecting the school board's request for an increase to $279 million.

Following an unrecorded voice vote yesterday, the chairmen of the council's seven standing committees agreed to review the departmental budgets under their supervision in search for the 1 percent cut. They are scheduled to report at a meeting Thursday. Under normal council procedure, agency budgets are not increased beyond the mayor's proposal unless cuts or new sources of funds are found elsewhere.

Some chairmen, notably John A. Wilson (D-Ward 2) of the finance committee and Willie J. Hardy (D-Ward 7) of the housing committee, voiced doubts the money could be found in the way proposed by Dixon.

Barry's budget director, Gladys Mack, said it would be "very difficult to maintain sufficient services" in the other agencies if their funds were diverted to the schools.