William H. Draper III, a 53-year-old California venture capitalist, was nominated yesterday by President Reagan as chairman and president of the Export-Import Bank.

The bank facilitates exports by U.S. industries by making low-interest loans to foreign buyers and arranging loan guarantees and insurance.

Draper is a founder and general partner of Sutter Hill Ventures in Palo Alto, Calif. He was cochairman of the finance committee in the George Bush presidential campaign, and later became a fund-raiser in California for the Reagan-Bush ticket.

According to a press release issued by the White House, Draper's firm raised equity capital for "150 young manufacturing companies throughout the United States."

At Ex-Im Bank, Draper would succeed John L. Moore Jr., a former Atlanta attorney who was active in Jimmy Carter's 1976 presidential campaign. Moore plans to leave the bank Mar. 31 to join the Washington law firm of Surrey & Morris.

The Ex-Im Bank has been a target for Reagan budget cutters. The president's budget proposal gives the bank direct lending authority in fiscal 1981 of $5.2 billion, down $700 million from the proposed Carter budget. Reagan also proposes reducing loan guarantees and insurance from $8.6 billion to $7.6 billion.

During the Carter administration, some Ex-Im Bank board members were criticized for their traveling expenses. Under the proposed Reagan budget, travel and administration expenses would be reduced by $320,000 to $15.43 million in fiscal 1981.

Draper graduated from Yale College in 1950 and received his master's degree from Harvard Business School in 1954.

Before founding Sutter Hill Capital Co. 16 years ago, he was an associate of Draper, Gaither and Anderson, a venture capital firm, and previously a sales representative for Inland Steel Corp.

Draper is a board member of a number of companies and organizations, including the Draper World Population Fund, a Washington-based foundation established by his father to monitor population trends, especially in underdeveloped countries.