The Supreme Court, taking on what may be the most sensitive sex discrimination case yet, agreed yesterday to decide whether women can be excluded from military draft registration.

It will be the first time the court has considered the once unquestioned assumption that the draft is for men only. Last year Congress, approving President Carter's draft registration program, expressly rejected his proposal to include women.

That rejection, along with the exclusion of women from the original draft law in 1949, will be reviewed by the justices. A ruling would ordinarily occur in June or July, too late to affect the men born in 1962 who must register next month under current law. About 4 million 19-and 20-year-old men registered during the summer in the first round of required sign-ups.

If the court stirkes down the law, Congress then probably would have the option of including women or having no draft registration program. President-elect Ronald Reagan, who campaigned against the peacetime sign-up, could end the immediate controversy by canceling the registration program when he takes office.

Feminists see the all-male draft as one of the last frontiers of sex discrimination. While protecting women in some respects, they say, exclusion also stignatizes them as unfit. The challenge is also supported by opponents of any peacetime draft or draft registration, who see the case as a vehicle for eliminating the program.

Many conservatives and traditionalists are promising congressional action to remove the issue from Supreme Court jurisdiction if the justices rule that women must be included. The conservatives, led by Phyllis Schlafly, contend that such a ruling would be tantamount to enacting the Equal Rights Amendment, despite the opposition that has blocked its ratification by the states.

The court agreed to review the July decision of a three-judge panel in Philadelphia striking down the draft law because it distinguished between men and women without sufficient justification. The lower court rejected the government's argument that the need for "military flexibility" supported the exclusion of women. The draft registration program, the government argued, was to secure combat troops for an emergency mobilization. Since women are not permitted in combat, their call-up was unnecessary, the government said.

The challengers, a group of draft-eligible men who brought the suit during the Vietnam war, used government statistics and testimony to convince the three judges that the draft of women would, in fact, be necessary during an emergency and that, in any case, the government's reasons for excluding women were inadequate under a 1976 Supreme Court ruling requiring a substantial justification for legal distinctions between the sexes.

Justice William J. Brennan delayed the Philadelphia order in the case, Rostker vs. Goldberg, pending Supreme Court review.

The court's acceptance of the draft case yesterday, a second sex discrimination controversy, and other related cases earlier this year guarantee that the 1980 will be the year of the woman at the court.

The court also agreed yesterday to review the federal government's power to issue regulations prohibiting sex discrimination in the employment practices of federally aided educational institutions. The case stemmed from Seattle University's challenge to a Department of Education investigation of salary scales at it school of nursing.

The university successfully argued in lower courts that the government was exceeding it congressional mandate by usnig federal funds as a lever in such investigations.

Earlier, the justices decided to consider an affirmative action program for women and blacks in the California Department of Corrections and the constitutionality of statutory rape laws, which punish men for having sex with underaged women but impose no penalty on women for sexual relations with underaged men.

In another discrimination action yesterday, the court agreed to decide whether a federal employe from Maryland is entitled to a jury trial to decide her charges of age discrimination. Alice Nakshian, a former secretary for the U.S. Navy, filed the suit, Hidalgo vs. Nakshian, in 1978 when she was 62.