Beirut — After eight months of increasingly rocky relations with the Arab world, the Soviet Union has begun to try to rectify its role in the region. Slowly but methodically, the Kremlin is doing this in a series of moves:
* Increasing military aid to Syria.
* Resuming support for Iraq in the Gulf war.
* Hinting at resolving the Afghanistan crisis.
* Dispatching ''unofficial'' delegations, often headed by Soviet Muslims, to several countries, such as Algeria and Lebanon.
The moves follow a period that may have been the worst ever for Soviet interests in the Middle East, primarily because of the Kremlin's inability or unwillingness to do anything during the Israeli invasion of Lebanon.
Second, the Soviet leadership, then under the late President Leonid Brezhnev, also did virtually nothing to help Iraq, with which it has a treaty of friendship, when the tide of the conflict with Iran turned against Iraq last spring.
Its credibility had sunk so low that even the most radical factions of the Palestine Liberation Organization were expressing disillusionment.
PLO chief Yasser Arafat repeatedly appealed for at least verbal warnings that might force the United States to put more pressure on Israel last summer. But he received only ''greetings of solidarity'' and encouragement to ''continue the struggle in the name of revolutions around the world.''
Under the new Soviet leader, Yuri Andropov, the course has been changed to even the big-power balance in a region where the US was left with a de facto diplomatic monopoly.
The most blatant move was the sale to Syria of SAM-5 ground-to-air missiles, which have a range of up to 180 miles and could cover parts of Israel.
Perhaps more ominous on the ground is the presence of Soviet military ''advisers'' in Syria. Their numbers are estimated to be increasing as a result of the new weaponry that requires advanced technological expertise, according to high-level US sources.
Because of its position as a so-called ''frontline'' Arab state bordering Israel, Syria is an essential member of any overall peace plan to resolve the 35 -year-old Arab-Israeli conflict. Western envoys believe the Soviets provided the arms and advisers to increase their leverage over the already hard-line government of Syrian President Hafez Assad to help thwart - ''if necessary'' - the peace plan proposed by President Reagan last September. However, one top envoy said the emphasis was on ''if necessary.'' With prospects for the US plan now rated low, the Soviets may just be waiting for the collapse of the effort.
Western sources feel the Soviets are laying the groundwork - a ''warming up'' process - for a major push in mid-1983. Late last year, the new leadership expressed support for the Arabs' own peace plan formed at the Fez summit.
And it is viewed by US sources as ''no coincidence'' that the first chief of state received by Mr. Andropov after his elevation to power was King Hussein - whom the US is counting on as the kingpin of its proposals.
Meanwhile, the Soviets also resumed shipments of military equipment to Iraq, after the failure of a policy aimed at maintaining friendships with both sides in the 29-month-old Gulf war.
The Iranian squeeze on its communist-oriented Tudeh Party and public criticism of the Soviet Union were in part responsible, diplomats say. But Iraqi President Saddam Hussein's warming up to the US - with which it does not even have formal relations - may also have played a part.
The official version was reflected in a report from Moscow in the Egyptian magazine Rose el Youssef: ''The Soviets say that the situation has changed since it has become clear it is the Iranians who insist on pursuing the war.
''There had been continuous contacts on their part to reach an understanding with the Iranian government on stopping the war, but the latter insisted on its continuation. The Soviets therefore decided to resume their support for Iraq and clearly stand by it.''
Soviet indications of a willingness to resolve the Afghanistan crisis will also boost its image in the Arab world. Although not an Arab state, Afghanistan is a Muslim country, and the 1979 invasion led to widespread condemnation from Muslim Arab states.
In other more subtle ways, the Soviets have also attempted to raise their profile in the Middle East. A Soviet delegation made the first visit to Lebanon last week since the invasion. Although it claimed to be ''unofficial,'' the group was led by Mohammed Asimov, a Russian Muslim and a deputy of the Supreme Soviet.
The mission was technically one to ''strengthen the bonds of friendship'' with Lebanon. But Mr. Asimov showed no signs of reluctance in talking about politics.
In an interview published in a Beirut magazine, he said ''the American policy of pressure and contradiction invariably leads to failure. This is clearly indicated by the escalation of the struggle against American policy in the area.''
The Soviets clearly hope the Reagan plan will not succeed, since it would lead to unprecedented US influence in the region. It would also diminish Soviet hopes to push for new ties, particuarly in the Gulf states, which, with the exception of Kuwait, have been beyond the Kremlin's reach diplomatically and economically.