The 18,000 workers in the 12-story Columbia Plaza office building here are employed by Uncle Sam -- but their work space is owned by the oil-rich government of Kuwait in the Persian Gulf.

For that space, the U.S. government pays Kuwait $2.3 million a year.

Kuwait bought the building for $22 million in 1976 in the second year of the 20-year lease held by the American government. For the lease's remaining 18 years at sale time, the federal government's rent payments will approach $42 million.

And they could be higher -- if the U.S. chooses to exercise renewal options for an extra decade of tenancy.

The Columbia Plaza offices -- the complex's apartments are separately owned and currently involved in a condominium conversion controversy -- were obviously a good investment for the Kuwaitis. It was also an unusual one.

As a rule, according to financial experts, Arab money managers prefer to invest their oil profits in stocks, bonds and securities, which can be held in relative privacy and converted easily into cash.

Only in rare instances does an Arab government participate in a highly visible purchase, such as Columbia Plaza, that ties up capital for a long period and carries some responsibilities for continuing management.

"The Arabs are very publicity adverse," observed Jeffrey Arpan, of Georgia State University's Institute of International Business.

"They know all about American reaction to Arab investment. . . . It's the same kind of reaction that German and Japanese investors got right after World War II."

Arpan, who is co-author of a directory that lists 3,400 foreign-owned businesses in the United States, says that Arab investors account for "less than one half of 1 percent of all foreign direct investment in this country."

Direct investment refers to ownership of real estate and business properties, as opposed to indirect investment in such things as stocks and bonds.

While most of the Middle East oil kingdoms prefer to maintain low visibility in their investments, Arab investment does sometimes splash onto the pages of American newspapers. But those stories are mostly about purchases by flamboyant individuals rather than governments.

Two Saudi Arabian businessmen, Ghaith Pharaon and Adnan Khashoggi, rarely spend their money without attendant publicity. They invest in real estate, shopping centers, hotels, office buildings and banks.

Pharaon's Saudi Research and Development Co. owns 60 percent of the stock of the National Bank of Georgia, stock purchased from Bert Lance, former director of the U.S. Office of Management and Budget and Carter confidant. Through other companies he controls, Pharaon also owns 20 percent of the Main Bank of Houston and 32 percent of the Bank of the Commonwealth of Detroit.

Khashoggi, through his Luxembourg-based Triad Holding Corp., owns partial interests in such properties as the Arizona-Colorado Land and Cattle Co. and the Galleria Shopping Center in Houston.

Among other American properties thatt have been acquired in whole or in part by Arab countries or individual investors are the Kiawah Island resort in South Carolina, the Landmark Hotel in Las Vegas, the Baltimore Hilton, and the Ivanhoe Hotel in Miami.

Although estimates vary, the total value of such direct investments by Arab governments and citizens is thought to be well below $2 billion. But just as it is with icebergs, the visible part of Arab investments is small and the hidden portion is immense.

The best valuable estimates of total holdings by Arab countries in the U.S. is put at almost $51 billion.

Last April, according to the Treasury Department, the Persian Gulf countries owned $9.5 billion worth of U.S. Treasury securities, $4.5 billion in advance payment for U.S. military hardware, $3.6 billion worth of securities issued by such government agencies as the Federal Home Loan Bank Board and the Federal National Mortgage Association, $2.2 billion worth of corporate bonds and $6.4 billion worth of corporate stocks.

The investment portfolio's total value was $32.3 billion, according to Treasury's figures.