Mr. Vice-President, I've got Monhegan Island on the line

A telephone rings somewhere in the White House. ''This is Monhegan Island . . .'' A long pause as this registers at the other end. ''. . . in Maine.''

A burst of laughter rings out from some 100 Monhegan Islanders and visitors dressed in their Sunday best and packed like sardines in the dining room of the Island Inn. Young children and weathered lobstermen hold their breath waiting for Vice-President George Bush to come on the line.

''Maybe he's out to lunch,'' whispers June Day with a twinkling smile, referring to the sometime Maine resident.

''Dr. Ashley?'' Mr. Bush's voice squeaks over the amplified telephone speaker.

''Mr. Vice-President,'' replies Alta Ashley, the grande dame of the island, ''we wish you were here to join in this joyous occasion.''

''I do too,'' comes the reply, ''but I just wanted to congratulate you on this, ah . . . I assume we are talking about a quantum leap forward into the technological age.''

More laughter and applause, and someone shouts, ''Reverse the charges!'' The congratulations and celebration continue.

Dr. Ashley's joyous occasion and Mr. Bush's quantum leap June 9 marked the end of a long-distance legal battle waged by the 75 year-round residents with New England Telephone to have a regular link with the rest of the world.

This tiny Atlantic island is only 11/2 miles long by 5/8 of a mile wide, and lies 10 nautical miles from Port Clyde on the Maine coast. But for the past two years, Monhegan's only links to the rest of the world have been one radio telephone, local lobster boats, and the Laura B, a small ferry from Port Clyde to Monhegan Harbor.

So the Laura B's return from Port Clyde with guests for the big celebration was an event in itself. Half the town was at the dock to welcome visitors and unload duffle bags, mail bags, boxes of Irish oatmeal, French liver pate, Gourmet jelly beans, and flats of fresh fruit - mainly blueberries from North Carolina.

When the commotion died down and the TV minicamera from Bangor had enough footage of quayside color, islanders and visitors headed up past quaint, gray, weathered houses, to the festive lunch at the inn.

Between 1919 and 1958, Monhegan Island had two telephone lines to the mainland. The Coast Guard replaced the original underwater cable with a new one in 1958, and eight more phones were added. But islanders say the cable was laid out with kinks in the line and was damaged during storms.

Hurricane Emily put the cable permanently out of order in September 1981. The Coast Guard refused to repair the cable and New England Telephone refused to provide telephone service.

For two years, the lobstermen, artists, innkeepers, and residents of the island had the use of one radio telephone in the general store and ''wrote a lot of letters,'' says a year-round Monhegan.

An appeal by the islanders, led by Dr. Ashley and aided by lawyer Alan Stone, to the Maine Public Utilities Commission resulted in a favorable decision. New England Telephone agreed to install a microwave system by May 31, 1983. With each step, relations began to improve between the island community and the telephone company, says Mr. Stone. Indeed, there were hugs all around during the celebrations.

Each islander wanting telephone service agreed to make a contribution of $300 ($120 down and the rest tacked on to monthly bills) to begin service. New England Telephone actually had the lines and transmission and receiving towers for the sophisticated $800,000 microwave system in operation four days before the target date, according to spokesman Peter Gorman.

There are those, of course, who come to an isolated place such as Monhegan just to get away from ringing telephones.

''I don't need a phone!'' grumbled one artist passing in the opposite direction along one of the several dirt tracks lined with lilac bushes and apple trees that wind around the island and up the hill from the Island Inn.

Still, for many the new link to the mainland was cause for celebration.

Barbara Hitchcock says ''it was all so exciting'' that she put on a string of pearls and a black dress to make her first call at the stroke of midnight. One islander said Mrs. Hitchcock actually made her call before midnight, since her phone was busy when the phone company called to say the system was in service.

Asked if having the new telephones was going to change life on the island, Mrs. Hitchcock suggests that ''there will probably be fewer letters and more chubby people - since we won't be running down the hill to tell friends things; we'll just pick up the phone and dial.''