Moscow — The Kremlin is on a major law-and-order drive, drawing on police, civilian militiamen, and a figure long prominent in Soviet life: the informer. Official concern over public drunkenness and street crime - and other ''antisocial'' acts like absences from work - has been building for several years. Yet new Soviet leader Yuri Andropov has from the start made ''social order'' a particular priority.
The police seem to have got the message: In Moscow, 3 million fill-in cards have been printed for distribution to city residents. A visiting policeman asks whether residents have had any problem with neighborhood drunks or other unruly elements. He takes out a card, fills in his name and phone number, and asks his hosts to call in case of any such nuisances.
Krasnodar, a city near the Black Sea, has a more limited, but much more direct campaign to get citizens' help in keeping Soviet society in order. Apparently following up a 1981, Brezhnev-era experiment in Kiev, the authorities have printed some 10,000 cards in hopes some of the city's 500,000 inhabitants will use them to report misdeeds.
The vigilant civilian simply marks one of various categories of disturbances listed on the card - such as drunkenness or playing hooky from work - and names the offender. The informant need not sign his name.
In Kiev, respondents were instructed to stay anonymous. The cards read: ''We ask you to report, without mentioning your name, all cases known to you of violations of public order and the rules of socialist communal life, of persons leading an antisocial way of life, failing to work, or abusing alcoholic beverages, of problem families, and of adolescents who have given up their studies. . . .''
Informing on thy neighbor is not exactly new in the Soviet Union.
Although the practice is nowhere near so deadly now as in the Stalinist 1930s , conversations with Russians suggest that, in Moscow, at least one routine ''informer'' is quartered in each of the city's thousands of apartment blocks.
Much more irregular reporting on neighbors or work-mates by others also goes on, and it is sometimes encouraged by the Soviet news media.
Indeed, propagandists and schoolteachers still celebrate the memory of a 13 -year-old boy named Pavlik Morozov who, in 1932, denounced his father to Stalinist authorities as an enemy of the state. The boy's irate grandfather and cousin murdered him. But, as the tale is told, right won out when they, too, were shot by a firing squad.
Still, the experience of decades past seems to exert a cautionary tug on some officials. Shortly after Andropov became Communist Party chief, police began checking Moscow shops for people off their jobs without permission.
The campaign was called off after a few weeks. Officials said privately it had been decided on high that other approaches to reinforcing work discipline were more prudent.
Under the late Leonid Brezhnev, even the practice of informing, at least on alleged official culprits, seemed sometimes to unsettle the men at the top.
In his address to the national party congress in early 1981, Mr. Brezhnev stressed the value of letters from citizens to the party leadership, adding that many of these letters were critical of ''serious'' official shortcomings.
He added: ''I emphasize this concerns letters that are sincere and honest. As for all sorts of anonymous vilifications, the party stand is well known: There should be no room for them in our life. . . .''
Andropov wasted little time in conveying his hope for a general tightening of order: that is, for a crackdown on alcoholism, ''hooliganism,'' absenteeism, and corruption of all types. Within weeks after he became party chief, the Politburo raised the need for heightened ''state, labor, and production discipline.'' The statement directed the ''prosecutor's office and the Ministry of Internal Affairs . . . to take measures to strengthen law and order in town and rural areas, since these issues are raised with particular urgency in the letters of working people to officials.''
There is also a new emphasis on the role of ''volunteer militias.'' These are formed on farm or factory floor, with an assist from the official trade unions. Nationwide, they include some 10 million people, but 1 million are concentrated in Moscow. That works out to 1 in 8 of the city's residents.
Recent media commentaries have stressed the need for more vigilance on the part of these ''druzhiniki,'' whose main traditional jurisdiction has been to combat drunkenness and minor street crime.
When a Moscow radio interviewer in February asked a uniformed militia official how the volunteers could be made more ''active,'' suggestions included more specialization - with some detachments handling traffic violations, others, ''parasitism, absenteeism, drunkenness, and much more.''
In a recent series of sidewalk interviews, about half of the Muscovites questioned said they had been visited by local police asking whether there were any particular neighborhood nuisances.
All reported other signs of greater militia visibility since transition in the Kremlin: for instance, the posting of the local militia's phone numbers on apartment entryways. A man said he was stopped on a city sidewalk by a policeman and asked to name the precinct in which he lived. When he could not, he was taken to the precinct station, told the precinct number for future reference, then released.
Many Russians seem to share the Andropov Politburo's sense that it is time to get tough on various ''violations of order'' - particularly on public inebriation and crime, and on official corruption. The typical sidewalk response is to welcome the greater visibility and apparent activity of forces combating such nuisances.
As for the more muscular approach of Kiev and Krasnodar, facts are harder to come by. The Kiev office whose phone number was listed on the 1981 inform-cards was asked on July 1 of this year how the campaign was going. The man who answered listened to the query, said he would fetch the duty officer, then promptly hung up.