NEW YORK (AP) _ NCR Corp., pulling itself out of a computer-industry slump, said Monday its net income rose 7 percent and its revenues climbed 12 percent in the last three months of 1985.

NCR, of Dayton, Ohio, is the first big computer company to report its results for the end of 1985, and the company's chairman said its upturn might be an early sign of good news for the rest of the industry.

''From time to time we have been a leading indicator'' of industry trends, Charles E. Exley, the company's chairman and president, said in an interview.

NCR's new orders increased ''substantially'' in the quarter ended Dec. 31, setting the stage for a strong beginning to 1986, the company said.

''Present indications are that 1986 will be another good year for NCR,'' Exley said. However, he warned that a predicted decline in capital spending in 1986 could hurt, and noted that his prediction was somewhat more optimistic than ones made recently by the heads of International Business Machines Corp. and Digital Equipment Corp.

NCR said net income, revenue and orders all set records for both the fourth quarter of 1985 and the full year. It said earnings were helped by the declining value of the dollar against other major currencies.

Analysts said the company benefited from strong controls on costs. The earnings statement was in line with their expectations.

NCR's fourth-quarter net income was $133.2 million, up 7 percent from $124.0 million in the fourth quarter of 1984, the company said.

The company said it earned $1.34 per share, up 9 percent from $1.23 in the comparable period in 1984. The earnings per share rose faster than total earnings because the company reduced the number of outstanding shares through stock repurchases.

Revenues in the fourth quarter were $1.41 billion, up 12 percent from $1.26 billion a year earlier.

NCR, the former National Cash Register, said orders were especially strong in mainframe computers and terminals for banks and retail companies. It also makes minicomputers, personal computers and semiconductors, among other products.

Exley said the semiconductor business continued to be weak. He said the company is focusing on semi-customized chips, where growth potential is strongest, and would not rule out the possibility of eventually ceasing production of read-only memory chips for general use.

For all of 1985, NCR said net income reached a record $315.2 million, up 1 percent from $312.0 million in 1984. Its earnings per share were $3.15, up 5 percent from $3 in 1984. The 1984 figures do not include a non-recurring tax gain of $30.6 million, or 30 cents a share.

Revenue in 1985 was $4.32 billion, up 6 percent from $4.08 billion in 1984.

Peter Labe, an analyst for Drexel Burnham Lambert Inc., said he thinks NCR will enjoy a successful 1986, in part because of the expected introduction of such products as the 9800, a mainframe computer that can be expanded by the addition of modules.

''It's a tightly run company,'' said Jay P. Stevens, an analyst for Dean Witter Reynolds Inc.