General Motors Corp. has signed an agreement with one of the nation's largest mortgage companies that puts the auto company in the business of handling loans for housing as well as cars.

General Motors Acceptance Corp., which finances consumer car purchases through 10,500 GM auto dealerships, has reached an agreement in principle to service the $11 billion mortgage portfolio owned by Minnesota-based Norwest Corp., GM officials confirmed yesterday.

Norwest last year was the second-largest mortgage banking company in the United States, according to the Washington-based Mortgage Bankers Association. The ranking was based on Norwest's servicing of nearly $12.1 billion in mortgage loans in 1984, an association spokesman said.

GMAC's purchase of Norwest's mortgage servicing rights is part of a larger GM plan to diversify into non-automotive businesses. The nation's largest auto maker also wants to play a major role in the computer services, insurance and defense industries.

Norwest operates 55 "loan production offices" -- places that handle consumer applications for mortgage loans -- in 23 states. Norwest sells groups of those mortgages to investors to generate cash to make more loans. But the Minnesota company retains the right to service those loans.

Buying the mortgage servicing rights "is very compatible with the demonstrated strength of GMAC," which has $55 billion in assets, said John S. Andrews, spokesman for the auto maker's finance company.

Norwest Corp. last year reported net earnings of $69.5 million ($1.90 a share), down from $125.2 million ($4.05) in 1983.