A telephone conversation about the Falkland Islands crisis April 9 between President Reagan and an airborne Secretary of State Alexander M. Haig Jr. was intercepted because neither chose to use a scrambler telephone, administration sources said yesterday.

A transcript of the 3 1/2-minute conversation between the two was published yesterday by columnist Jack Anderson, who said he was given a tape by a source he has declined to identify.

The conversation, which took place as Haig was flying from London to Buenos Aires and Reagan was on a working vacation in Barbados, briefly reviews Haig's efforts at shuttle diplomacy between Britain and Argentina, but involves nothing of a top-secret nature.

Government communications specialists said last night it is not unusual for the president or a Cabinet secretary to forgo the use of a secure telephone and talk over open lines, especially if the connection is between two remote spots.

The sources said the intercepted conversation was initiated by Haig, who had a secure telephone on his Air Force plane but elected not to use it.

"They do it all the time," one government security official said, despairing of the reluctance of officials to use the large, cumbersome, box-like apparatus that scrambles conversations at one end and decodes them at the other.

Another administration source said both men were advised before the conversation that they were not using a secure line, and both agreed that it was not necessary.

The specialist speculated that Haig and Reagan talked over a high-frequency connection that would be easy for ham operators to intercept.

Joseph Spear, an associate of Anderson, told The Washington Post yesterday that, after Anderson received the tape, one of his reporters spoke with the Secret Service as part of the effort to establish its authenticity.

Spear said the reporter was informed that the Secret Service was "totally aware" of the problem of such intercepts. A Secret Service spokesman yesterday denied that account and denied knowing anything about the Reagan-Haig intercept.

Anderson said his source provided him with a transcript of a conversation and a tape. He said he believes they are of two separate conversations because the transcript includes comments from both men, while on the tape Haig's responses are inaudible because of interference or static.

A transcript of the taped conversation:

Reagan: Al, hello Al. I'm glad the British fleet doesn't move that fast. You must have been in the air for about 12 hours now and pause . There's going to be an uphill struggle. Did you get any idea as to whether the emotion that you met in your meetings goes out beyond the Parliament to the people as well? Over.

Haig: Ten-second pause.

Reagan: It sounded as if there was not much acceptance of the multinational presence here. Are there any variants of that you think she might go for? Over.

Haig: Thirteen-second pause.

Reagan: Oh, that sounds good. Incidentally, that submarine of theirs, ah, do you think it's apt to go ahead with retribution and sink anything within the 200 miles and would that be enough to vindicate them? Over.

Haig: Fourteen-second pause.

Reagan: Oh, that's good. Well, I won't ask you to speculate on any next steps because I know you haven't talked yet there in Buenos Aires. But, in those talks, if it's helpful at all, why, don't hold back on making me the bad guy and insisting on restraint if that's necessary? Over.

Haig: Nineteen-second pause.

Reagan: Okay. Well, I know it's a tough one and an uphill fight. Just let us know if there's anything at this end that we can do to be of help. And, ah, good luck. Pause Over.

Haig: Eight-second response.

Reagan: Just did today. Pause Had a good swim in this ocean that you're looking down on. And it was wonderful. Well, okay, I'll make it over and out then, or unless you've got something else. Okay, good luck.