After yesterday's sentencing, the women returned to the Mission; this time, their petition was accepted.
Prosecutors said they were arrested in March after ignoring police orders to disperse.
The four were acquitted of disorderly conduct, resisting arrest, and obstructing government administration. They had faced up to a year in jail if convicted of all counts.
"We should never have been on trial in the first place," Sheehan said in a statement after the verdict. "It's George Bush and his cronies who should be on trial, not peaceful women trying to stop this devastating war. This verdict, however, will not stop us from continuing to work tirelessly to bring our troops home."
Sheehan's 24-year-old son Casey was killed in Iraq on April 4, 2004. She has since emerged as one of the most vocal and high-profile opponents of the war, drawing international attention when she camped outside President Bush's Texas ranch to protest the war.
The women, calling their campaign "Women Say No To War," had hoped to give the petition to Peggy Kerry, the mission's liaison for non governmental organizations and sister of Senator John Kerry, Democrat of Massachusetts, as they had in 2005.
Peggy Kerry refused to meet with the women in the presence of Sheehan and the media. She testified that the presentation seemed like a publicity stunt.
The women ignored police orders to leave and were reading the petition aloud on the sidewalk when officers arrested them. The women sat on the sidewalk and were carried to patrol wagons.
The women asked for an apology yesterday when they returned to the US Mission and resubmitted the petition.
They were met by Peggy Kerry and Richard A. Grenell, the mission's director of external affairs, who said the women apparently were unable to find the original petition and handed over a document bearing 32 signatures.