WASHINGTON--The Supreme Court, embarking on a term laced with controversial issues, said yesterday it will decide whether police nationwide may use sobriety checkpoints in trying to curb drunken drivers.

The case accepted by the court, which poses the question of whether police officers may use checkpoints to spot drunken drivers, presents the latest test of strength for the Court's newly solidified conservative majority.

Michigan courts struck down that state's sobriety checkpoint program as an unconstitutional invasion of privacy, but courts in other states have upheld virtually identical police tactics.

In its usual start-of-term flurry, the Court issued orders in more than 1000 cases--denying review to most and agreeing to study 22. They will be among 150 or so disputes to be decided by the end of the term in July.

But beyond the day-to-day business of the nation's highest court, the nine justices are looking ahead to a term in which they have agreed to decide thorny right-of-privacy arguments in three abortion disputes and their first "right-to-die" controversy.

Last year's court term was perhaps the most publicized in decades, as the conservative court turned to abortion and civil rights issues which have not been substantially changed since an activist, liberal court of the 1960s and 1970s first ruled on their constitutionality.

The Court yesterday also heard arguments in a Yonkers, N.Y. desegregation case centering on four city council members who voted against a judge's order to pass a legislative package designed to lure subsidized housing to the city's white neighborhoods.

In addition to that civil rights case, the justices on their first day also:

. Agreed to decide in an Illinois case whether public employers may be forced to put aside partisanship when hiring, promoting and transferring employees.

. Turned down the appeals of eight organized crime figures from New York City convicted in the 1979 assassination of crime chieftain Carmine Galante and two of his associates.

. Left intact Maryland's revocation of a $300,000-a-year tax break for a men-only golf club that has counted presidents and members of Congress among its members.

. Refused to spare an evangelical Christian group in Lenox, Mass., from having to return $5.5 million donated by a wealthy ex-member.

. Rejected Alaska's attempt to stop offshore oil and gas exploration in Bristol Bay. The state had argued that an oil spill there could do more environmental harm than the massive Exxon Valdez spill last March.

. Allowed states to criminally prosecute employers accused of neglecting the health and safety of their employees. The justices, without comment, let stand a ruling in an Illinois case that federal workplace regulations do not bar such state prosecutions.

The use of police sobriety checkpoints in Michigan was attacked shortly after state police began using them in 1986. The program was modeled after one used in Maryland.