GEORGE SHULTZ is giving the Reagan administration's new Mideast peace initiative its first international airing. The initiative is an invitation to a proceeding that at this stage is to unfold under American aegis, not under the American-Soviet sponsorship foreseen in the now-sidetracked proposal for an international conference. That alone was enough to put off Mikhail Gorbachev. The plan is ''inconsistent,'' he said, and does not engage all sides. Still, he reported that he and the American secretary of state had agreed to ''resume the exchange of opinions after George Shultz makes a trip to the Middle East.''

Mr. Shultz has been taking Mideast soundings. In Israel, the first response was polarized, which is good because consensus means paralysis. It will take a hard fight for a more reasonable view -- the view of the Labor opposition, led by Shimon Peres -- to win through. Meanwhile, Mr. Shultz has been getting a good exposure to the unreasonable view of the government. Most of Prime Minister Yitzhak Shamir's Likud bloc still embraces the annexationist aims so thoroughly undermined by the Palestinian resistance. Likud rejects the basic American tenet of the negotiated exchange of land for peace. But even Mr. Shamir is on the defensive, fearful that talks on West Bank-Gaza autonomy might slide irreversibly into early talks on the final status of the occupied territories -- as the American plan intends -- but not eager to take on the onus of stopping the negotiations before they even get started.

The ''moderate'' Palestinians, in their familiar confusion, stood up Mr. Shultz, who patiently explained -- as he will have to explain a hundred times again -- how self-defeating it is for them to shun a role in the making of their own political destiny. The key Arab governments involved, Syria and Jordan, heard out the secretary, but basically hid behind the Palestinians' skirts. The PLO leadership is now attempting to catch up with the stone-throwers. Evidently the PLO thinks this is the moment to draw the United States beyond its acknowledgment of unspecified ''legitimate Palestinian rights'' into approval of Palestinian ''self-determination,'' code for statehood. But this is not the moment -- not if the United States wants, as it does, to give Likud incentive to look at the new facts the stone-throwers have created in the West Bank and to keep a space open for Labor in next November's Israeli elections.

The violence goes on in the West Bank, and Palestinians are dying. But American diplomacy is stirring, and there is a thrust to it and some hints of show-me receptivity to it too. Nobody else seems capable of getting something moving.