Arnautoff was born in Oakland, California, and attended the University of San Francisco where he played on the men's soccer team from 1975 to 1978.
In 1979, he signed with the Edmonton Drillers of the North American Soccer League.
He also played two seasons with the Philadelphia Fever of the Major Indoor Soccer League.
The Moscow Games were the first to be held in Eastern Europe and were boycotted by the US and a number of other countries in reaction to the Soviet invasion in Afghanistan the year prior.
Victor Arnautoff, Russian-American painter and professor of art, is Peter's grandfather.