In the first test of new federal firing procedures under the Civil Service Reform Act, the government has been forced to reinstate (with full back pay) an air traffic controller who had been dismissed for allegedly smoking marijuana off duty.

The decision by an arbitrator is the first award under new disciplinary guidelines established by President Carter's overhaul of civil service personnel practices. The U.S. employe, a controller at St. Thomas in the Virgin Islands, was fired by the Federal Aviation Administration. FAA said he had been seen off duty with a group of people who were believed to be smoking the illegal substance.

The Professional Air Traffic Controllers Organization took the case and elected to go to an outside arbitrator rather than to the Merit Systems Protection Board. The reform act gives workers the option of going the regular appeal route, through the board, or having the case heard by an arbitrator if the worker is covered by a union contract or agreement.

PATCO officials said FAA based its dismissal action on the testimony of an unnamed informant who did not come forward at the hearing. PATCO's agreement with the FAA states that a "preponderance of evidence" standard must apply in dismissal cases. The arbitrator, James A. Morris, said in this case he felt that "the evidence should be clearly sufficient to support a conclusion that the matter asserted is most probably true rather than false."

A PATCO official here said the union spent about $3,000 on the case, and chose the arbitration route because arbitrators "view the penalty of discharge to be the industrial equivalent of the death penalty," and they believed the arbitrator would demand conclusive proof to sustain the charge.

The PATCO official said that rigid mental and physical requirements must be met by air traffic controllers, whose primary function is "to provide safe, orderly and expeditious flow of air traffic." In layman's terms, he said, "the bottom line is to make sure that airplanes don't run into each other."

The controller was reinstated this summer with about five months' pay. FAA has no plan to appeal the arbitrator's ruling, an official said yesterday.