John K. Darr, chief financial officer of the troubled Financial Corp. of America, has resigned to accept a senior position with another financial institution.

Darr, a member of FCA's three-man president's office, will continue to assist the company during his transition, FCA Chairman and Chief Executive Officer William Popejoy said yesterday.

FCA, parent company of American Savings and Loan Association, is the nation's largest savings and loan holding company with assets of about $31 billion. During the summer, rumors of financial trouble caused it to lose many depositors. As interest rates rose, withdrawls of investment deposits increased.

The company was also forced by the Securities and Exchange Commission to restate its earnings for the first half of 1984, resulting in an unexpected $107 million second-quarter loss.

Former FCA chairman Charles Knapp resigned in August under pressure by the federal Home Loan Bank Board, reportedly because federal regulators were alarmed by his allegedly imprudent policies and the company's dangerously high rate of growth. It has 122 branches in California, 33 loan production offices in 10 states and 25 institutional sales operations throughout the country and overseas.

Popejoy has promised bank board officials he will limit the company's annual asset growth to less than 18 percent, the savings and loan average.