American Telephone & Telegraph Co. announced plans yesterday for an offering of 15 million shares of common stock, the largest in its corporate history.

The huge communications company said it hopes to raise enough money from the stock sale to lower its debt ratio and finance expansion and improvement of services.

AT&T said that underwriters will have an option of purchasing 1.5 million more shares if there is that much demand for the issue. The underwriters have not yet been announced.

AT&T stock is the most widely held in the country, with more than 3 million shareowners and more than 770 million common shares outstanding.

The company said that the offering exceeded all previous offerings in terms of the number of shares to be sold. If the price of AT&T stock remains reasonably solid, it also may exceed previous offerings in dollars raised.

The company's last common stock offering was in November 1977, when it raised $718 million through the sale of 12 million shares.

Trading on the New York Stock Exchange in AT&T stock was halted shortly before the announcement, a customary practice. When trading resumed, the stock was down 1/8 to 57 3/4. The stock closed at 56 1/2 yesterday with a high of 58 1/4, a low of 56 and volume of 549,600.

AT&T said it was making the stock offering to increase its financial flexibility and to provide growth for the Bell System. The company said the proceeds will be used for general corporate purposes, including retiring debt coming due, advances to subsidiaries and associated companies and for investment in those companies.

A spokesman said the company hopes to reduce its debt ratio from 46.3 percent of total capital to 46 percent.

Underwriters will be named when AT&T completes registration with the Securities and Exchange Commission later this week.