THE usual visitor to Quebec's remote Anticosti Island goes there in quest of deer or Atlantic salmon. But an effort has been started to attract summer tourists: hikers, campers, bird-watchers, fossil hunters and part-time anglers who would enjoy an offbeat sojourn in a wild and lovely spot.

Situated in the Gulf of St. Lawrence between Quebec's North Shore and the tip of the Gaspe Peninsula, Anticosti is 140 miles long and 35 miles wide, with a maximum altitude of about 1,000 feet.

During a recent four-day visit to La Loutre lodge, which is at the mouth of the river of the same name on the island's southwestern end, I was immediately aware of an almost unbroken coniferous forest. I was told that there were substantial stands of birches and aspens on other parts of the island, which are accessible by hard-packed dirt roads. But my itinerary, which centered on deer hunting, left no time for wide-ranging explorations.

Over the centuries, Anticosti has had many owners. Its original human inhabitants, either American Indians or Inuits, were first there about 3,500 years ago.

As the centuries went by, various Amerindians visited the island from time to time. The first permanent white settlers, who were French, arrived late in the 17th century.

Anticosti entered a new era in 1895, when Henry Menier, the French millionaire ''chocolate king,'' bought it from a forest-products company for $125,000.

When Menier died in 1913, his brother Gaston took over, and in 1926 he sold out to the Wayagamack Pulp and Paper Company for more than $6 million. The island was owned by two other pulp and paper companies before it was taken over by the Quebec Government in 1974.

At the time of Anticosti's sale by Gaston Menier, the island's population had reached a high of 800 people, all dwelling in Port-Menier at the island's west end. Current year-round residents, all in Port-Menier, number slightly more than 300.

Salmon were entering Anticosti's rivers long before humans arrived, but it was Henry Menier, who apparently had a vision of a private sportsman's paradise, who brought the deer to the island.

Wasting no time, he imported 100 of them from the mainland in 1896, and 120 more in 1897. Anticosti's present deer herd is estimated at 70,000 to 100,000 animals. Menier's other successful introductions included moose, red fox, beaver and varying hare. His failures included elk, caribou and American bison.

A subsequent private owner stocked muskrats, whose domed houses in the marshes about Port-Menier testify to the success of that endeavor. And the province has released a few spruce grouse on the island.

The island's ruffed grouse show little or no fear of man. The half-dozen I saw didn't saunter off until I was within three feet of them. How they got there isn't clear, because the shortest flight from the mainland is more than 20 miles. Grouse aren't supposed to be able to remain airborne for much more than a mile.

The hunting and fishing lodges scattered about the periphery of Anticosti account for most of the island's economic activity. Some are run by private outfitters. Others - the lion's share - are operated by the Societe des Etablissements de Plein Air du Quebec, a crown corporation devoted to building up the province's outdoor-recreation enterprises.

It is this corporation that is now striving to bring summer tourists to the island. Information about the island's various summer offerings may be had by writing La Reserve d'Anticosti, C. P. 179, Port-Menier, Anticosti, Quebec GOC 2YO, Canada. The telephone number is (418) 535-0156.

Those who go to Anticosti for deer hunting (one may shoot two deer of either sex) or salmon fishing exclusively, pay $2,000 or more for less than a week of their sport.

The usual way to reach the island is to fly from Mount Joli on the Gaspe to Port-Menier, although in summer, there is a small ferry that carries both vehicles and people.

A summer visitor who stays at one of the corporation lodges - the aforementioned La Loutre is one - for a week will be charged about $1,000. But housekeeping cottages can be had for less than half that amount. The cottage rate is based on occupancy by at least four persons.

All of these arrangements include a pickup truck for traveling about the island and round-trip air fare to and from Mount Joli. There are also campgrounds where one may pitch a tent. Rental vehicles are available.

The island has 27 salmon streams, of which the Jupiter and the Riviere aux Saumons are the best. Those who wish to angle for trout and salmon on the island must buy the appropriate provincial licenses.

There is a strange timelessness about Anticosti. On one gray day, I puttered along the shores of Lac Longue. More than five miles long when it is full, it had shrunken considerably, leaving conifer-clad islands rearing through the fog above the dried lake bottom.

Several hundred yards from the water at the edge of the forest was a metal lifeboat from an oceangoing vessel, the Faillete Brown, whose rusting hulk lies on the beach near the mouth of La Loutre.

At the lake's southern end, a dried-up creek bed contained flat pieces, a quarter-inch to half an inch thick, of sedimentary rocks, some of which had neat little holes in them. The holes in those rocks - rocks that could be about 300 million years old -marked where shelled organisms dwelled when the island was on the floor of an ancient sea.

Flocks of ducks I couldn't identify - the fog was thick and it was getting dark - flew over me as I stood on the shore of Lac Longue. I could hear Canada geese calling.

Returning to the lodge, where a red and a silver fox were always present at dawn and dusk waiting for a handout, I learned from Yves Morin, a biologist, that brook trout of 3 to 4 pounds and more were in Lac Longue.

I thought of them, of the eight good-sized salmon I had seen resting on the bottom in one of La Loutre's upper pools, of the island's other trout streams and lakes - it has sea-run trout, as well - and began to daydream of a trip there next year.

My daydream included paddling a canoe, weather permitting, along the shore of the island, making camp at river and creek mouths, doing a bit of angling, and observing the gray seals and whales that visit Anticosti's coastal waters in summer.