The Reagan administration's record on arms control can be summed up in Winston Churchill's phrase ''arm to parley.'' From the start, the emphasis has been on demonstrating the will to improve United States and NATO nuclear arsenals, thereby convincing Moscow that it could not win an arms race and should negotiate seriously.

An opponent of previous treaties, the President had promised to offer a new strategic weapons reduction plan ''immediately.'' It was a year and a half, however, before this happened. The administration's first START (strategic arms reduction) proposal was ambitious: to reduce both sides' ballistic missile warheads by one-third, with sharp reductions in land-based missiles. Since the Soviet Union has more of its strategic warheads on land-based missiles than the US, Moscow rejected such deep cuts.

Faced with a possible defeat of the MX missile in Congress, the administration in 1983 changed its START proposal to raise the ballistic missile sublimit. A few months later (and, again, under pressure from lawmakers), it added a complicated provision to ensure that older weapons would have to be retired as new ones were deployed.

Meanwhile, parallel talks at Geneva were being held on intermediate-range nuclear forces (INF). In response to the Soviet deployment of triple-warhead SS- 20 missiles aimed at Western Europe, NATO in 1979 had agreed to pursue arms control talks in this area while preparing to deploy 108 new US-built Pershing II ballistic missiles and 464 low-flying cruise missiles in Europe.

Mr. Reagan first proposed that NATO forego deployment of new missiles in exchange for Soviet removal of all SS-20s (and older similar missiles) from Asia and Europe. Citing the French, British, and Chinese missiles aimed at them, Moscow insisted that it had to keep some medium-range nuclear weapons.

In private discussions with his Soviet counterpart, US INF negotiator Paul Nitze developed the ''walk-in-the-woods'' idea. This would have limited the Soviet Union to 75 SS-20s (with a total of 225 warheads) aimed at Europe; in exchange, the US would deploy no Pershing IIs and only 75 cruise-missile launchers with a total of 300 warheads. This was not well received in Washington , however, and was eventually rejected by Moscow.

Just before the scheduled deployment of the first US missiles, the administration softened its ''zero option'' somewhat. But by then, it was too late. The Soviets walked out of the Geneva INF talks as promised when the first NATO missiles were deployed last December. Moscow also refused to set a date for the resumption of the START talks.

Reagan has offered to ban chemical weapons, but there has been no progress toward a comprehensive nuclear test ban. Administration officials also have suggested that the Anti-Ballistic Missile Treaty might have to be changed to accommodate the President's strategic defense (''star wars'') proposal.

Critics say squabbling between the Pentagon and State Department on arms control has prevented progress and also indicates a lack of presidential leadership.

Defenders of the President note Soviet intransigence and the three different Soviet leaders Reagan has had to deal with.

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