The court, however, sentenced the four - including a policeman and a finance ministry official - to one year in jail for illegal possession of an automatic weapon.
The guilty verdict can be appealed.
Prior to the US-led invasion of neighbouring Iraq, speculation grew that US forces were stationed in the kingdom to mount attacks against Baghdad.
The government denied that.
Later, it acknowledged there were several hundred American military personnel in Jordan, but said they were not stationed there to mount an attack on Iraq.
US troop presence
Rather, they were assigned temporarily to help set up anti-missile batteries in eastern Jordan to protect the kingdom from Iraqi rockets.
During the 1991 Gulf war, Iraq fired 39 Scud missiles that flew over Jordan into Israel.
In Monday's brief hearing, court president Colonel Fawaz Buqur said the court found the four defendants "innocent of terror conspiracy charges since the prosecution has failed to prove that a crime had been committed against state security".
"Innocent ... since the prosecution has failed to prove that a crime had been committed against state security"
Colonel Fawaz Buqur,
military court president
He defined the crime as conspiring to attack American forces in Azraq and Ruwaishid, two desert towns near the Iraqi border.
Null and void
Buqur said the crime became null and void when the government declared there were no American forces in Jordan.
Buqur said the State Security Court, however, found the four men - three of whom have been in police custody since late last year and the finance ministry official who remains at large - guilty of possessing a Russian-made machine gun.
He sentenced each to one year in jail.
The three defendants in custody, who pleaded innocent at the outset of the trial on 11 March, reacted joyfully when the acquittal was pronounced.
Wearing dark blue prison uniforms they shouted "Allahu akbar!" meaning God is the greatest.