The South African diamond and minerals empire controlled by Harry F. Oppenheimer is rapidly becoming a major investor in mining, energy and commodities companies in the United States and Canada.

Through a subsidiary called Minorco, a holding company based in Bermuda, the South African firms headed by Oppenheimer have invested hundreds of millions of dollars in North American coal, uranium, gold, copper and other important minerals, and have developed the capital resources to finance further acquisitions.

Documents filed with the Securities and Exchange Commission show that dozens of mining and minerals companies throughout the United States and Canada are wholly or partially controlled by the South African interests. Although no figure for the value of their holdings is available, a new study by a New York researcher says the South African group has been one of the biggest foreign investors in the United States over the past two years.

The investments reflect a long-range corporate strategy that Oppenheimer developed in the 1970s and spoke about publicly at the time. Oppenheimer sought to expand his companies' stake outside South Africa for economic and political reasons, and to do it he transferred assets now worth more than $2 billion to the Bermuda subsidiary to circumvent his country's restrictions on the export of funds.

The policy of investing in North America "is no accident," corporate research specialist Ruth Kaplan says in a report to be published by The Africa Fund. "It offers a stable area politically and economically; it is an area rich in mineral and energy resources and the company will realize a high return on successful investment." In addition, she said in a telephone interview, "it allows them to position themselves outside South Africa in the event of trouble there."

In addition to investments by Minorco, Kaplan said, "a total of 144 separate investments in North America by the Anglo group have been identified; 108 of these investments are in the United States (in 32 states) and 36 are in Canada."

Business relationships between U.S. firms and South Africa have been controversial for many years because, critics say, they contribute to the economic power of the white-minority regime in South Africa and support its apartheid racial policy. Most attention from church groups, institutional investors and stockholders, however, has focused on investments in South Africa by U.S. corporations. The extent of South African investment in the United States--which has the same effect of forging links of mutual interest between U.S. and South African companies--has been little noticed.

A few critics who have examined South Africa's growing involvement in the U.S. economy have objected that the investments are financed by the fruits of apartheid and that they strengthen the power of the ruling minority.

For example, the Interfaith Center on Corporate Responsibility, a Protestant church group that monitors corporate performance on social and environmental issues, plans to offer a stockolders resolution at the forthcoming annual meeting of Citicorp to get Citicorp Chairman Walter Wriston off the board of directors of Minorco. Citicorp, parent of the giant Citibank, has continued to make loans to South Africa when most other major banks have stopped doing so.

Oppenheimer, one of the world's richest men, has a longstanding reputation as a liberal, at least in the South African context, using his personal wealth and power to oppose apartheid and improve living conditions for his country's blacks. Nevertheless, Timothy Smith, director of the Interfaith Center, said Oppenheimer is still a "profiteer" whose fortune was built on the backs of low-paid black miners.

Oppenheimer is chairman of the Anglo American Corp. and of its affiliate, De Beers Consolidated Mines Ltd., each of which owns a substantial interest in the other.

According to Kaplan, whose findings are confirmed by SEC records and by investment experts in the Commerce Department, "Anglo American is the biggest single economic factor in South Africa . . . the Western world's largest producer of gold, diamonds and platinum." De Beers "operates a monopoly in the diamond trade, marketing 80 percent of the world's diamonds, including the Soviet Union's."

Oppenheimer is chairman of Minorco, an acronym for Minerals and Resources Corp. Also on the board of directors, besides Wriston, are Robert Clare, a partner in the New York law firm of Shearman & Sterling, which represents Citibank; Felix Rohatyn, head of the investment banking firm Lazard Freres, and Cedric Ritchie, chairman of the Bank of Nova Scotia.

Minorco, which is wholly owned by the Anglo-De Beers interests and their subsidiaries, is the largest stockholder in Phibro Corp., the giant New York commodities trading company. Minorco, according to SEC records, owns 18.5 million shares of Phibro stock, or 27.2 percent of all outstanding shares, a stake worth almost $450 million. H. Ronald Fraser, president of Minorco, sits on Phibro's board of directors.

Phibro, the world's largest publicly owned commodities trading company, had worldwide sales of more than $25 billion last year, a fourfold increase over its sales five years earlier. It is also the sole owner of the New York investment house of Salomon Brothers, which Phibro acquired last year for $800 million.

That acquisition, Kaplan noted, offers Minorco "potential new sources of capital and different ways to get at it," because of Salomon Brothers' expertise at corporate fund raising and merger management.

Phibro became a separate company last year when it was spun off from the former Engelhard Minerals and Chemicals Corp., now known as Engelhard Corp. Minorco is the largest stockholder in Engelhard, with 7.4 million shares, or 27 1/2 percent. Engelhard in turn owns a network of petroleum and minerals subsidiaries, and controls a major segment of the market for kaolin, a clay used in making, among other things, porcelain.

Another branch of the complex Anglo American family tree runs through Consolidated Gold Fields Ltd. of Britain. De Beers secretly acquired 29 percent of Consolidated's stock in 1980, then transferred its holdings to Minorco in exchange for Minorco stock.

Consolidated Gold is the largest stockholder in Newmont Mining Co., one of the largest U.S. copper producers. Consolidated owns 22.4 percent of Newmont's shares and has an option to increase its stake to 26 percent.

Newmont in turn controls an extensive network of oil, uranium, zinc and cement companies, including sole ownership of Atlantic Cement Co., Newmont Oil, and Carlin Gold Mining Co. of Nevada and majority interests in Dawn Mining Co. and Magma Mining Co.

Newmont also owns 27 1/2 percent of Peabody Coal Co., the biggest U.S. coal company, which indirectly gives Anglo American one of its largest stakes in U.S. energy resources.

Another skein of the Anglo American web runs through Canada, where Anglo Amcan of Canada, a wholly owned subsidiary of Minorco, owns 45 percent of the stock of Hudson Bay Mining and Smelting Co. According to data compiled by Kaplan, the chairman and chief executive officer of HudBay is H. Ronald Fraser, the same Minorco executive who sits on the Phibro board.

HudBay controls the Terra group of fertilizer and chemical companies and group of seed, fertilizer and agricultural warehouse companies in the Midwest farm states, according to Kaplan's report. Amcan and HudBay also hold a controlling interest in the Francana oil and gas companies in Canada, she said.

The Anglo American group's pattern has been to leave the operating management of its acquired or controlled companies in place, keeping an eye on its investment through its network of interlocking directorates.

"Anglo's control of its subsidiaries and affiliated companies is not organized in a hierarchical structure but rather as an associated group of companies with interlocking connections," Kaplan's report says. "In effect, Anglo gets maximum control with a minimum investment."