COLUMBUS, Ohio, March 22— John W. Bricker, a Republican Governor who ran for Vice President on the party's ticket in 1944 and served in the United States Senate for two terms, died today. He was 92 years old.

''I join with all Ohioans in mourning the death of John W. Bricker,'' said Gov. Richard F. Celeste.''Ohioans will long remember his leadership as Governor and United States Senator in the 1940's and the 1950's.''

Mr. Bricker last sought elective office in 1958, when he suffered an upset in his bid for a third Senate term at the hands of Stephen M. Young. Since then, he had devoted his time to his law practice. ---- Four Decades in Office Starting in 1952, John William Bricker set himself up as defender of the Constitution - by trying to amend it. Over the years he persistently offered more than twenty versions of a proposal to limit the treaty power of the President and Senate.

For the strapping, sonorous, silver-haired Ohioan, the Constitutional campaign, though unsuccessful, created far more impact than his 1944 race for Vice President with Gov. Thomas E. Dewey of New York. That political effort was drowned out in the fourth-term landslide vote for President Roosevelt.

Mr. Bricker was a twin. His sister Ella and he were born Sept. 6, 1893, on a farm in Pleasant Township, Ohio. He taught for a year after his graduation from high school. Then he earned his college degree at Ohio State University and, after studying law for one year, passed the bar examination in 1917.

Rejected as a World War I enlistee because his heart had only 55 beats a minute instead of about 72, he became an athletic instructor at an Ohio Army camp. Later he got into the Army as a chaplain and first lieutenant, ordained by his Congregational Christian Church on condition he not preach.

After the war Mr. Bricker finished his law course. In 1920 he became solicitor of Grandview, Ohio; in 1923, Assistant Attorney General of Ohio; in 1929, member of the state Public Utilities Commission and in 1933, Attorney General. Sought Presidential Nomination

In 1938 he was elected Governor, Mr. Bricker became the state's first Republican to serve three consecutive gubernational terms. He attained national fame for transforming a $40 million deficit to a $75 million surplus in six years, despite increased budgets for education and welfare.

Unsuccessful in his quest for the 1944 Presidential nomination won by Mr. Dewey, Mr. Bricker became the Vice Presidential nominee. He said he was ''more interested in defeating the New Deal philosophy of absolutism'' than in becoming President himself.

One month later the America First party nominated him for Vice President, with Gerald L. K. Smith, an extreme nationalist, for President. Mr. Bricker repudiated the move, calling it ''demagogy, religious intolerance and racial prejudice.''

Mr. Bricker was elected to the Senate in 1946 and was re-elected in 1952.

In the 1952 Republican convention it fell to Mr. Bricker to withdraw the name of his colleague, Senator Robert A. Taft of Ohio, from nomination to allow Dwight D. Eisenhower a unanimous nomination for President.

His wife, the former Harriet Day, died June 1, 1985. He is survived by his son, Jack Bricker, a Columbus lawyer, seven grandchildren and a niece.

John Bricker