Mr. and Mrs. Jack E. McGregor of Bedford, N.Y., formerly of Chevy Chase, Md., have announced the engagement of their daughter, Nancy Dangerfield, to Thomas Warham James, son of Dr. and Mrs. G. Sargent James of Lincoln, Mass. A September wedding is planned.

Miss McGregor, who just completed her first year at Harvard Law School, is a magna cum laude graduate of Barnard College, where she was elected to Phi Beta Kappa. She has also attended Sidwell Friends School in Washington. Her father, a former Pennsylvania senator and founder of the Pittsburgh Penguins, is president of the Hampton-Douglas Corp. in Bedford, N.Y. He is also chairman of Caribbean Water Resources, Ltd., a former vice-president and general counsel of Potomac Electric Power Company in Washington, and later became executive vice-president of Carey Energy Corp. in New York.

Mr. James, a management consultant with Bain & Company in Boston, Mass., is an honors graduate of Harvard College and the Harvard Graduate School of Business Administration. He has written for The Boston Globe and was formerly with the Business Day staff of The New York Times. His father, vice-president of AVCO Everett Research Laboratory in Everett, Mass., is a research physicist who holds numerous patents in the application of lasers to enrich uranium for the generation of nuclear power plant fuel.