A federal judge ruled yesterday that the Reagan administration has flouted its obligation to help desegregate the Chicago public school system, and he ordered the government to find at least $14.6 million to fund the city's integration plan.

U.S. District Court Judge Milton Shadur wrote that since Jan. 21, 1981, its first full day in office, the administration and its Department of Education have made "a continuous effort to strip away all means by which they could fulfill" the terms of a 1980 consent decree worked out between the Chicago Board of Education and the Department of Justice.

That agreement, signed under Shadur's supervision in the last days of the Carter administration, called for both sides to "make every good faith effort to find and provide every available form of financial resources for the desegregation plan."

The $14.6 million represents the minimum federal expenditure Shadur will require for the 1983-84 school year. School board attorneys will go back to court Aug. 10 to seek unspecified tens of millions of dollars more for that period.

The Chicago plan does not include mandatory busing. It combines magnet schools, voluntary transfers and the redrawing of some school district lines to help even the racial mix in the city's more than 500 public schools.

Shadur's ruling gives the government until Aug. 8 to say where it will get the money for its share of the desegregation costs. Until then, Shadur has extended a temporary June 8 order forbidding the government to spend or commit tens of millions of dollars in certain federal education funds.

"It's an unprecedented victory," Schools Superintendent Ruth B. Love said after the ruling, "but it's one we would have preferred not to have taken. We want to be in a cooperative mode with the federal government, not adversarial."

The legal dispute stems from the Reagan administration's decision to combine desegregation aid and 28 other education programs into block grants given to states to spend at their discretion. Attorneys for the school board argued successfully that the block grants tended to be diverted from desegregation spending.

Because Shadur's ruling turned on the government's acceptance of the 1980 consent decree, which is unlike any other in the nation, the case was not expected to lead to widespread attacks on the block-grant system.

The government was considered virtually certain to appeal the decision.