The Reagan administration enters 1983 with what some experienced officials see as a reasonable chance for reaching a nuclear arms control agreement with the Soviet Union. But a big question mark, as one official acknowledged, is whether the administration can "get its own act together" to seize that opportunity if it is presented.

Setting aside for the moment the question of whether Moscow will negotiate in good faith to reduce the level of its nuclear-tipped missiles, interviews with U.S. government officials suggest that Washington is faced with these internal problems:

* While President Reagan has frequently stated his interest in reaching arms control agreements, there is no one at the top level of the administration who is strongly advocating finding a compromise with Moscow, is familiar with the arcane details of arms control and has substantial influence with the president.

What this means is that ideas on how to get agreement tend to enter the administration from the bottom rather than at the top, and therefore are more subject to veto before they reach the Oval Office.

* The most recent hopeful sign, say officials who believe an agreement is possible, is that Secretary of State George P. Shultz, who has only been in office five months, is becoming more involved in the issue. But Shultz is hampered, some specialists say, by such things as continued strong opposition by some conservative lawmakers to the proposed appointment of Richard Burt as assistant secretary of state for European affairs.

Burt is a State Department specialist on arms control, and Shultz has recently put his prestige on the line in support of his ultimate confirmation by the Senate. But it is not at all clear yet that Burt will be confirmed.

* The question of Burt's future is symbolic, some officials say, of the broader question of whether this highly conservative administration, with its conservative base in Congress, can in fact reach out to Moscow for a fair arms control agreement on one hand without causing a rebellion among some of its supporters.

It is because Shultz has such a low-key style and is so close to the president that many officials believe, if the secretary and the president are so inclined, that he can help pull off an arms control agreement despite the divisiveness of the issue.

* At the moment, sources say the senior administration official "carrying the water" for arms control is Paul H. Nitze, the chief U.S. negotiator in U.S.-Soviet talks in Geneva aimed at limiting medium-range missiles based in Europe. Nitze, who will be 76 next month, is widely viewed as the best informed and most experienced American specialist in this field and is also the one who probably has the best feel for where compromise with Moscow is possible.

Yet, officials say, it is not clear who, if anybody, is listening to Nitze. On at least one occasion, Nitze was stopped by the White House from continuing an informal exploration of a compromise in which the Soviets and the United States would be left with some medium-range missiles in Europe.

* Finally, sources believe that one key to whether the Reagan administration will ultimately move on arms control lies in the fate of the Pentagon's budget and what happens to such new weapons as the proposed intercontinental-range MX and intermediate-range Pershing II missiles.

Officials acknowledge that it is a self-serving argument to say that fair and prudent arms control agreements can be achieved only if the Reagan rearmament program goes ahead. But they say the administration is convinced that Moscow will not be more flexible until the Soviets come to believe that Reagan is winning the long-term battle over the defense budget.

Washington and Moscow are engaged in two sets of talks in Geneva that are going on simultaneously. Aside from those involving Nitze on medium-range missiles based in Europe, there are also Strategic Arms Reduction Talks (START) on limiting the intercontinental-range missiles and bombers based in the United States and Soviet Union.

Yesterday, retired Army Lt. Gen. Edward L. Rowny, who heads the U.S. START negotiating team, told an interviewer on the NBC-TV "Today" show that "I think the odds are probably 50-50" that the two superpowers will reach an agreement on strategic arms in 1983.

But officials following the arms issue believe that if an agreement is to be reached next year, it is more likely in the talks on European-based missiles or perhaps in a combined solution to both negotiations.

Next year is certain to be crucial because by the end of 1983, the United States and its NATO allies are committed to begin installing 572 new U.S. missiles in Europe meant to offset some 600 Soviet missiles, including 333 new triple-warhead SS20 weapons, already installed.

That deployment is certain to cause huge controversy and protests in western Europe and the Soviets seem determined to try to stop the deployment. Thus, some officials argue, if the White House can reach an agreement with Moscow before then it would head off a potentially wrenching crisis for the alliance and give the administration an important political victory at home and abroad.

The key issue, however, is what kind of a compromise, if any, can be worked out. It is this question that does not seem to be getting much top-level attention at the moment, according to some sources.

There is some speculation, however, that one possible compromise could involve an agreement by the Soviets to destroy as many of their missiles as it takes to bring the number of warheads down to the level that existed prior to the introduction of the new SS20s, which touched off the western concern.

In other words, NATO might forgo deployment of new missiles, if the Soviets would go back to the general balance of power that existed earlier, some officials speculate.