Prosecutors dropped all charges yesterday against Charles W. Rinker Jr., the Arlington minister and political leader who had been indicted for conspiracy and fraud in an alleged scheme among officials of a Youth Pride Inc. real estate spinoff company to steal and misappropriate thousands of dollars from a federally funded housing project they managed.

Rinker, former chairman of Virginia's 10th District Democratic Committee and one-time candidate for the Arlington County Board, appeared in U.S. District Court in Washington yesterday where prosecutors said they decided to drop the charges after Rinker successfully completed a polygraph examination.

After the hearing, he declined to give details about his polygraph examination, conducted earlier this month by FBI agents. He said he had made no agreements with prosecutors in exchange for the charges being dropped, although he said he expects to be called as a witness in the case.

"I'm overjoyed that it's over with," said Rinker, surrounded outside the courtroom by his family. "They finally realized that I'm innocent. I've been telling the truth all along."

Rinker said he had offered to submit to a lie detector test on the allegations numerous times and that government attorneys finally agreed to conduct the six-hour examination March 3.

Prosecutors, who have said they regarded Rinker as a minor figure in the case, declined comment yesterday.

Yesterday's action before Judge John Garrett Penn leaves Mary Treadwell, former executive director of the self-help enterprise Youth Pride Inc., as the sole remaining defendant in the case. Treadwell, who is scheduled to go on trial April 19, has denied any wrongdoing.

Three other defendants have pleaded guilty to charges in the 1982 indictment. They are Robert E. Lee, former general manager of P.I. Properties; accountant Ronald S. Williams and Treadwell's sister, Joan M. Booth. Johnny Mickens III, Youth Pride's former chief financial officer, was not named in the indictment but has pleaded guilty to charges of income tax evasion in a separate case.

Williams, Mickens and Lee have all agreed to testify for the government.

Treadwell's attorney, John W. Nields, said his client "is just overjoyed for her friend and colleague." Nields declined further comment.

Rinker, Lee, Treadwell, Williams and Booth were charged in a 30-count indictment with portraying P.I. Properties to government officials as a nonprofit business but actually using it to fund their own profitmaking enterprises and to pay personal expenses.

The indictment alleged that operating funds from the Clifton Terrace apartments in Northwest Washington were diverted to finance renovation work on private homes, to decorate the office of an advertising firm, to make down payments on real estate for other profitmaking enterprises and to pay personal legal fees.

Rinker began working for Youth Pride Inc. in 1969, and later took on posts with other Pride spinoff companies. He left Youth Pride and the other businesses in April 1978. He has said he worked for the companies out of a desire to promote social justice and never suspected wrongdoing.

He said last year that he left the companies because "I just basically felt that the businesses weren't going to be successful and the dreams I had worked so hard for weren't going to come to fruition."

Last March a coalition of Northern Virginia Democrats and civic leaders organized a defense fund to help Rinker pay his legal costs. Andy Marks, one of Rinker's attorneys, said the two lawyers representing Rinker had agreed to take the case without a fee. He said the defense fund had raised about $20,000 and that most of that money would go to pay expenses connected with the defense.

The federal investigation into P.I. Properties began in October 1979 after a series of articles on the firm ran in the Washington Post. Rinker was not a subject of those articles.