President Carter's deep involvement in the Middle East has come whistling back at him and his political fortunes like a poison-tipped boomerang.

Foreign policy in general and his achievements in the Middle East in particular were supposed to be Carter's strong cards in a reelection campaign that would necessarily skip over his failure to develop and put across a coherent domestic policy. The peace agreement between Egypt and Israel that he negotiated had to be seen as a towering accomplishment by any standard.

But the 1,001 tales that seem destined to tumble out about Billy Carter's Libyan adventures, and the continuing efforts by Israeli politicians to drive Egyptian President Anwar Sadat into a corner on Jerusalem have made the Middle East more a source of embarrassment than of succor for President Carter.

In one sense, Carter's campaign strategists undoubtedly still cling to a desperate hope that foreign policy can rescue their chief from his present standing in the polls. To win, they are banking on Ronald Reagan making the kind of foreign policy flub that Gerald Ford made in the 1976 debate when he said that Eastern Europe was independent of Soviet domination.

Such hopes look increasingly forlorn as Carter's plummeting domestic support begins to play into the international political game, making it even easier for leaders abroad to ignore of undermine those parts of Carter's foreign policy they oppose. This, in turn, will add to the image of U.S. importence abroad under Carter.

Israeli Prime Minister Menachem Begin's refusal during the past three months to do anything to ease the pressure on Sadat over Jerusalem has come at a time when Cater is powerless to exert any pressure on Israel.

Whatever Begin's intentions, his recent actions on Jerusalem and the West Bank are cutting the ground not only from under Sadat but also from Carter's ability to emphasize in the campaign that his main foreign policy accomplishment, the Camp David peace treaty, is alive and well.

This is likely to increase suspicions here that Begin and many other Israelis would not be unhappy to see Reagan replace Carter in the White House. Carter's on-again, off-again flirtation with the Palestinian cause already has infuriated them and many American Jews.

Sadat is also being hurt, although less seriously, by the Libya scandal in Washington. The White House meetings with Col. Muammar Qaddafi's diplomatic representatives here and the Carter family connection indirectly extend some new importance and legitimacy to the Qaddafi regime.

From Sadat's perspective, Carter must be seen as having sought help from Qaddafi, the one leader whom Sadat truly believes to be criminally insane and with whom the Egyptian can never be reconciled even under the elastic terms of Arab politics.

Thus far, Sadat has publicly taken the high road on both the Libyan and Jerusalem problems, saying nothing on the former and carefully avoiding any criticism of Carter for not restraining Begin on the latter. The Egyptian media have been noticeably quiet on the Libyan case.

The first signs that the Libya scandal is beginning to have some effect on the standing of the Carter administration abroad emerged yesterday as official Soviet and Chinese newspapers informed their readers that the president's reelection chances were being affected by the uproar here.

"These days the entire country is talking about the scandalous history, with its questionable financial deals," Pravda reported in Moscow. "But the main reason for the disillusionment lies deeper.Preelection promises are broken, the country is gripped by economic decline, inflation, mass unemployment."

The New China News Agency, perhaps reflecting fears by Chinese leaders that Reagan would move for closer ties with Taiwan if elected, told readers that the "affair of Billy Carter" was attracting increasing attention as the Democratic Party convention approaches, but then cited public opinion polls that indicated that most Americans think it is unfair to blame President Carter for his brother's behavior.