Israel's decision to push ahead with annexation of the Golan Heights appears to be a show of toughness intended to compensate for recent diplomatic setbacks. Prime Minister Menachem Begin's Cabinet decided Dec. 14 to introduce annexing legislation into the Knesset (parliament). If a full Israeli annexation of the territory - seized from Syria in the 1967 six-day war - is enacted, it will enormously complicate the Middle East peacemaking process.
The likely fallout would include:
* A widespread Arab outcry against the United States for having failed to prevent its Israeli ''client'' from taking this step - with the US as well as Israel being in the dock at the United Nations. Syria has already asked for an urgent meeting of the Security Council to consider the situation.
(US officials privately expressed surprise and concern at Israel's action, but so far, the White House and State Department are witholding public comment.)
* Complete alienation of Syria at the very time of growing outside recognition that Syria must be included in negotiations for an overall settlement of the Arab-Israeli conflict.
* Possible Syrian military retaliation. This seems less likely on the Heights themselves than in Lebanon, where much of Syria's military is concentrated as a ''peacekeeping'' force and where Syria's President Assad can count on the qualified support of the Palestine Liberation Organization. Syria has a treaty of friendship and cooperation with the USSR.
* Neutralization of any new effort by Arab ''moderates'' - such as Saudi Arabia or Jordan - to edge the Arab world generally to acceptance of the state of Israel.
* Increased isolation in the Arab world of the new Egyptian President Hosni Mubarak who would have to be guarded in any protest - lest he give the Israelis a pretext for not completing their scheduled final withdrawal from Sinai next April.
Israelis - and particularly Prime Minister Begin - do not take easily to slights or setbacks. Retaliation is part of their makeup. And it is significant that the Golan decision was the first major announcement from a Cabinet meeting after the combative Begin's release from the hospital after a thigh injury.
He probably felt that a show of Israeli toughness was needed after these rebuffs on the international and domestic fronts:
* Failure of the Israeli-supported effort in the US Senate to block President Reagan's proposed sale of AWACS planes to the Saudis.
* Persistence of the US tilt toward Saudi Arabia - in Israeli eyes - as indicated by Crown Prince Fahd's planned visit to Washington next month.
* Failure so far to secure the withdrawal from Lebanon of Syrian missiles deployed last May. Mr. Begin is publicly committed to getting the missiles out, hinting at the use of force if necessary. But he has apparently been stalled by the diplomatic efforts of US special envoy Philip Habib.
* Perception by the Israeli public generally that Israel was short-changed by the US in the ''memorandum of understanding'' on strategic cooperation between the two countries signed earlier this month in Washington by their defense ministers.
* Acceptance under US pressure of European troops in a Sinai peacekeeping force.
The Jerusalem Post wrote recently that President Reagan's attitude ''appears to have changed. Israel is no longer the twinkle in his eye. . . . The President and his advisers already have come to regard Israel as America's constant pain in the neck.''
Under these circumstances, Mr. Begin and his Cabinet colleagues may have concluded they had nothing to lose and may have something to gain by showing that they too can play hardball.