n. A society in which corporations have substantial economic and political power.
Since at least 1775, when Isaiah Thomas published his eye-witness account of the Battle of Lexington, the Worcester area has harbored many important activists for social change. Some of them, as in Thomas' siding with rebels against British rule, challenged the dominant social structures of their time. Others, in conflict with the status quo, had a vision of a society quite different from violent, imperial corpocracy that we know as American culture.
—Michael True, “Abby to Abbie: remembering Worcester's activist tradition,” Sunday Telegram, April 01, 2001
1987 (earliest)
The house on Francis Avenue, an elegant Victorian built of dark, thin-set brick, sits in bosky gloom at the edge of the Harvard campus. John Kenneth Galbraith, professor, former U.S. Ambassador to India, belletrist and author of The Affluent Society, The New Industrial State, The Anatomy of Power and a number of other economic polemics that, taken as a whole, constitute the most damningly articulate assault on what has come to be known as the American corpocracy, is at home.
—Augustin Hedberg, “Lights! Camera! Economists!,” Money, October 01, 1987
This term combines the word corporate and the suffix -cracy, which means "rule; government; power.' (A similar, if hideous, term is corporatocracy, which dates to 1995.) Its recent popularity is due at least in part because of its frequent appearance in the influential 1998 book, Corporation Nation, by Charles Derber. However, the term had been around for a few years before that, as shown by the earliest citation.

Note, too, that this term actually began life with a different meaning: It was a blend of the words corporate and bureaucracy, and it was coined by Mark Green and John F. Berry in their 1985 book, The Challenge of Hidden Profits: Reducing Corporate Bureaucracy and Waste. This sense achieved buzzword status in the late 80s and was the favorite corporate put-down of liberals and even some conservatives. This sense has had a desultory career since then, and the latest citation I could find was from 1997, so the end appears nigh for what Michael Kinsley once called a "barbarous neologism."