Members of the biggest federal civil service union will probably begin nationwide voting within the next few weeks on whether to admit, and actively recruit, uniformed personnel from the Army, Navy and Air Force.

The action, which would be the first serious attempt to unionize the U.S. military, is expected to be formally proposed next week. It will come from a special study group set up by the American Federation of Government Employees which now has about 280,000 all-civilian members, and bargaining rights for nearly 600,000 white-collar and blue-collar federal workers.

Last September, the gian AFL-CIO union convention altered its civilian-only constitution and directed its new president Kenneth T. Blaylock, to go ahead with the military sign-up if he thought it was necessary.

Blaylock said at the time that he would study the idea and would back unionizing drives in the military if he thought it would help strengthen the pay, working conditions and political clout of his civilian members - and be well received by the 2 million-plus enlisted military personnel who would be eligible.

Earlier this year, Blaylock appointed a three-member committee - composed of AFGE regional vice presidents - to study the feasibility of organizing the military. Although an official announcement has yet to be made, there were strong indications yesterday that the committee would endorse the military sign-up, and ask the union's national executive council to recommend a nationwide referendum of AFGE members.

Top union officials were playing "I've Got a Secret" yesterday at a Washington Hilton meeting of local AFGE leaders from Defense bases. But talks to the group by several AFGE officials - plus off-the-record comments from some AFGE leaders - indicate that the military organization question will go to the council next week.

Head counters say the council will vote to recommend the referendum with AFGE members voting within their own locals. At least two, and maybe all three of AFGE's top national officers would strongly back the idea of military members.

President Carter said last week that he is against unions in the military.But he added that he would not actively promote legislation pending in the Senate and House that would outlaw any union activity in the armed forces. The President also said - even as the AFGE group was meeting - that there were no "serious" discussions by any unions relating to organizing the military. There will be next week.

Ironically, the idea of recruiting military members came to AFGE leaders, in part, as a device to club the Ford administration over the head. Ford was considered antifederal employee by the big union, which endorsed the Carter-Mondale ticket. AFGE officials said frankly they would use the threat of organizing the military to "keep the White House guessing" as to their intentions, and perhaps buy more favor from Ford if he were re-elected.

Now the AFGE is having problems with President Carter that it did not foresee from candidate Carter. Among them, the new President has endorsed a Ford administration ploy to sharply whittle back the system used to pay the government's half million blue-collor workers. About 55 per cent of AFGE's membership comes from mechanical, trade and craft workers in government, most of them in the Defense Department.

The presence of AFGE locals - from SAC air bases and the Pentagon to Navy installations in the Pacific - means that the manpower and machinery for recruiting military personnel is already in place should the union decide to expand to military members.

Many of the union's presently all-civilian members oppose the idea of organizing the military. The major argument is that it would dilute services the union now supplies to them. Others are concerned that a congressional backlash - especially if a military sign-up flopped - could hurt the union's lobbying on Capital Hill and anger the President.

The official green light should come this week from the union's ruling council, and then ballots will be going out to civilian members asking if they want to bring in the military.