Federal grants-in-aid to state and local governments would be reduced by $9.8 billion or about 10 percent to total about $81.4 billion in the fiscal 1983 budget President Reagan has proposed.

About $3.9 billion of the cuts are in income support programs for individuals that are managed by state and local governments--such as Medicaid, child nutrition, welfare and housing programs.

An additional $5.9 billion would be sliced from the assortment of education, jobs, rehabilitation, energy assistance and other programs of federal aid to states and cities. Reagan has proposed consolidating many of these categorical aid programs into seven new block grants that would give states greater flexibility in determining how the money is spent.

The proposed fiscal 1983 reductions would come on top of $3.5 billion in cuts the administration got Congress to approve last year. In the two previous decades, federal spending for these programs and entitlements had increased at an annual rate of 11 percent.

The administration said its reform and paring-down of federal regulations would allow state and local governments to achieve savings through more efficient management of programs, but it also suggested that they might have to raise local taxes.

"The increased tax base available to state and local governments due to the recently enacted federal tax cuts, and the existing and proposed block grants, allow the states the capacity to meet their greatest priorities and needs," the budget message said.

New block grants Reagan proposed would be for vocational and adult education, education for the handicapped, employment and training, rehabilitation services, child welfare, refurbishment of rental apartments and the administration of welfare programs.