About a third of American workers in a Social Security survey said they had retired and sought benefits because they were tired of working, while only a quarter cited illness as the major reason that they stopped working.

The survey, published in the Social Security Bulletin, covered a sample of 9,000 workers who went on the Social Security benefit rolls in the year ending May 1981.

It found that more than three-quarters of the retired workers started drawing benefits before reaching 65. About half the men and three-fifths of the women began receiving benefits at 62, the age at which workers can first retire on Social Security.

The survey showed that about a third of the married women questioned stopped work at least three years before beginning to draw benefits. Among men, only about10 percent stopped working as early as three years before receiving their first benefits, and among unmarried women, 14 percent.

The survey asked those who had stopped working the major reason that they had quit their last job.

About one-third -- 33.8 percent -- said they wanted to retire or were tired of working or did not like their jobs. Among men, the proportion retiring because they were tired of working was two-fifths, among women one quarter.

The second major reason was ill health, cited by about 25 percent in most age groups.

This was a sharp change from a similar survey taken in 1968, when 54 percent of all men aged 62 to 64 cited health as the major reason that they had stopped working.

Here are some of the other reasons cited as by workers for leaving their last jobs:

* About one out of 10 men and one out of eight women said their primary reason for leaving their last job was that business was bad or they had been fired.

* Only 7 percent of the men and3 percent of the women said that they left because of compulsory retirement rules.

* The report said "relatively few 5 percent of the men and 2 percent of the women reported that eligibility for Social Security benefits or any other pension was what prompted them to leave."

* Only a handful of men cited family obligations (3 percent) as the major reason for stopping work, but the figure for women was much higher: 17 percent.