House investigators have laid out a series of ethics accusations against Democratic Rep. Charles Rangel, the once-powerful tax-writer who is one of the most senior members of Congress, presenting his party with a new complication in advance of the fall elections.

Mr. Rangel, of New York, will have the opportunity to defend himself at a public trial before the House ethics committee beginning next week, according to a statement Thursday from the panel, formally known as the House Committee on Standards of Official Conduct....