ITALY'S CURRENT WAVE of street violence and terrorism is having curious effect on political alignments. It's making the Communists look increasingly like a party of law and order. When the Communists have to choose between the police and the violent demonstrators of the ultra-left, they stick with the police. Among the voters of the uneasy middle class, that raises the Communists' respectability quotient.

But, unfortunately, there's also another and broader effect of these shootings and kidnappings. It aggravates a mood of cynicism and exasperation among the great law-abiding majority of Italians, who view it as further evidence of their government's inability to govern. The Communists are now part of the government in every sense but the most narrowly legalistic, and the party's leaders are aware that this general condemnation of the national administration is rapidly coming to include them.

In May, the Red Brigades assassinated the president of the Turin Bar Association in an attempt - a successful one - to intimidate prospective jurors in a trial of 53 accused terrorists. In early June three prominent newsmen were shot in the legs by gunmen who explained that they were striking a blow against the forces of psychological oppression. Last week there was another rash of shootings and explosions. As you would expect, terrorist groups often move into common criminality. Kidnapping for ransom has become a thriving industry.

It's in the court system that the Italian government's response breaks down. These courts can take years to resolve the most ordinary of cases. Those that lie beyond the ordinary may never be resolved at all. The classic example is the bombing of a bank in Milan in 1969. Fourteen people were killed and 90 hurt. An anarchist was arrested but, as years passed, new evidence seemed to implicate a right-wing organization. No one has been convicted, and the trial has now been lost in a fog of conflicting theories and suspicions of political manipulation. Americans take for granted the broad public benefits of having inquiries driven relentlessly to a conclusion on the public record, in courts and before legislative hearings. The Italian experience indicates the cost to society when that kind of exposure is repeatedly deflected.

Last week the Communists joined the other major parties in a joint program for the present emergency. It gave a good deal of emphasis widening the power of the police in dealing with suspected terrorists and establishing preventive detention. The terrorists are trying to demonstrate, of course, that Italian society is falling apart.That's wrong, so far; Italian society is tough and remarkably shock-resistant. But a continued high level of street violence carries sinister implications for the future. The immediate test for the government is whether its courts can be made to bring cases efficiently to verdicts. Further failure would have a devastating effect on public morale. Trust in a system of justice is no small element in the glue that holds a country together.