Federal workers who are angry over paying anywhere from $12 to $45 per month to park will have their day in court. The American Federation of Government Employees union has asked U.S. District Court here to invalidate parking fees inposed on the bureaucracy last year by President Carter.

Under the Carter plan, U.S. workers at hundreds of installations are now paying half the commercial fee for parking. Next fall they will begin paying the same rates charged in parking lots nearest their offices. A number of installations have been exempted from pay-parking, either because of their remote locations or because public transportation is inadequate. Still about 30,000 U.S. employes here who once parked free -- if they could get a sticker and the space -- now pay. Pay parking does not, of course, apply to most congressional offices.

AFGE has argued that the pay parking program is improper, and that it was imposed by presidential whim, without benefit of an executive order or an act of Congress. Earlier this year U.S. District Court Judge Harold H. Greene denied a government motion to dismiss the AFGE anti-pay parking lawsuit. He said that while federal workers do not have property rights to office parking spaces, they may have a case on the grounds that the pay parking edict was imposed improperly, that is administratively. AFGE has asked him to dismiss the pay parking program entirely. He may, and he may not. Whichever side loses is expected to take the case to a higher court. Until the issue is settled, federal workers will continue to pay to park -- unless their agencies can wangle an exemption in the meantime.

Federal workers who hope for a change in the pay parking program from the Reagan Administration are probably hoping in vain. People at the Reagan transition office downtown on M street are paying almost $5 per day to park.