C. Austin Fitts, the unconventional and polished former investment banker recruited by Housing and Urban Development Secretary Jack Kemp to run HUD's troubled housing programs, resigned yesterday after little more than a year on the job.

Fitts, 39, is leaving HUD after months of turbulence that rocked the agency in scandal and strained relations between her office and the developers, bankers and interest groups who did business with HUD. Recently, sources said, her relationship with Kemp had also faltered.

One HUD source attributed the resignation to "a difference in management styles and philosophy" and said Fitts's departure was mutually agreed upon yesterday when she and Kemp decided "it wouldn't work out."

Fitts did not return phone calls seeking comment last night.

Fitts was assigned to repair the bulk of HUD's troubled programs, including the Federal Housing Adminstration and the mortgage coinsurance program, which together were responsible for millions of dollars in bad loan losses during the Reagan administration.

Fitts, whose resignation was accepted immediately, will be replaced by Arthur J. Hill, president of the Government National Mortgage Association (Ginnie Mae), a government-owned corporation that purchases mortages from private lenders and packages them into securities.

Until he arrived at HUD last August, Hill, 42, was president and chief executive officer of Peoples National Bank in Miami.

Fitts's tenure at HUD was defined by the scandals that came to dominate the department's agenda. She acknowledged in interviews that damage control was her first order of business.

Kemp has lost several top aides in the 20 months that he has been at HUD. Last month, Sherrie Rollins left her post as assistant secretary for public affairs, and in September, deputy assistant secretary for multifamily housing Jim Logue will leave to join the National Council of State Housing Agencies. Earlier this year, former Cincinnati mayor Kenneth Blackwell, one of two deputy undersecretaries, left the department to run for an Ohio congressional seat.

Housing industry officials who have watched HUD closely in recent months have joined some career HUD employees in complaining that HUD has become gun-shy and unlikely to take on marginal projects or follow through on executed contracts.

Fitts, on the other hand, was known for the unconventional solutions she proposed for the department's problems. Early on, she suggested that the department change its name to HOME and that the government conduct bargain sales to rid itself of excess foreclosed properties that proved to be a drag on the FHA loan portfolio.

Those ideas, contained in a memo sent to Kemp, were publicly repudiated by HUD Undersecretary Alfred A. Dellibovi and quietly set aside without action.

Before coming to HUD, Fitts worked in New York for Dillon, Read & Co. investment bankers since 1978. She received her masters in business administration from the Wharton School at the University of Pennsylvania and was a member of President Bush's campaign finance committee in 1988. She also contributed to Democrats over the years, including $500 to Jesse Jackson in 1988 and $1,000 to Bruce Babbitt's presidential campaign in 1987.