LEAD: A small but growing rock music movement is spreading across the cities of India. Rock fans are turning to young Indian musicians who are writing original songs and music instead of merely reproducing the hits of American and other Western stars like Bruce Springsteen, Madonna, Tracy Chapman and Sting.

A small but growing rock music movement is spreading across the cities of India. Rock fans are turning to young Indian musicians who are writing original songs and music instead of merely reproducing the hits of American and other Western stars like Bruce Springsteen, Madonna, Tracy Chapman and Sting.

''Every month, we're out on tour for 15 or 20 days,'' said Uday Benegal, the 22-year-old lead singer of Rock Machine, a sextet that is one of India's most popular groups. Last year, Rock Machine was sent by the Indian Government to the Soviet Union as part of a large celebration of Indian crafts, arts and culture.

Grudgingly, the Indian cultural establishment is recognizing rock and pop music played by Indians as part of the country's cultural diversity. This acceptance is also new among Indian audiences. A Hit With 5,000 Copies

''The audiences are increasing, the records are selling better and the groups are showing their ability to compose original music,'' said Raj Pandit, the 57-year-old chief executive at CBS (India). Although the market for Indian rock music has grown more than tenfold in the last decade, the size of the market is still tiny compared with that in the West: an original recording that sells more than 5,000 copies here is regarded as a hit.

The major themes in Indian rock music are universal, but the songs are often particularly relevant to Asia. Singers like Remo, who is from the southern Indian state of Goa, for example, sing of corrupt politicians in India and the problems of bad telephones. But they also praise the vitality of a city like Bombay, India's major movie and cultural center, as in one Remo song: You're a crazy town, You're a merry-go-round, You're king and clown, Never lie down, Bombay City!

The big cities provide good audiences but it is the East of India, where there are large Christian communities and where English is widely spoken, that Indian rock music is finding its largest audience.

''You get terrific vibes in Calcutta and the Northeast because they understand your music, they're sophisticated and have a wonderful, natural musical flow,'' said Mr. Benegal, the lead singer of Rock Machine. The group's first album, ''Rock Renegade,'' has sold more than 10,000 copies in six months.

''Two years ago, an Indian band couldn't draw an audience of more than 800 people,'' said Mahesh Tinaikar, a guitarist with Rock Machine. ''Now we get 10,000 in a stadium.'' 'Audiences Are More Receptive'

Mr. Tinaikar, whose his hair reaches his shoulders and who wears a T-shirt and faded jeans, said that until recently Indian fans felt that local bands ''were not good enough.''

''Now things are changing,'' he said. ''The audiences are more receptive.''

With bigger audiences for concerts, Indian rock groups' incomes have improved too. Rock Machine nets about 20,000 rupees, or about $1,400, for a 90-minute show. Local organizers pick up all expenses: airline tickets, hotel rooms, stadium rents. Yet rock music as a calling is still regarded as insecure at best in India and Rock Machine is among only a handful of groups that have turned full time to music. Other rock singers and players work at a job or play traditional music at clubs, parties and hotels to support themselves.

And singers here must still compete with powerful names like Michael Jackson (whose album ''Bad'' sold 150,000 copies in India) and widespread audiocassette piracy.

''Naturally, people are going to prefer a Michael Jackson album or a Bruce Springsteen record over an Indian singer, no matter how talented or good he or she is,'' said Vijay Lazarus, the vice president of Music India, one of three major recording companies in India. Mr. Lazarus pointed out that while the turnover in the Indian music market had grown from about $14 million in 1979 to $140 million these days, those who had largely profited were pirate companies taking advantage of light enforcement of copyright laws. Looking to U.S. and Britain

Most of the groups, even Rock Machine, have no full-time managers or press agents to set up and promote their concerts and they have to rely on local organizers to pay for their travel. But it's better than paying for their own shows, as they had to do when they began as a group about three years ago.

One common dream that drives all the Indian rock groups is making it big - and big for them is in the offices and recording studios of the giant music companies in the United States and Britain.

However, music executives like Mr. Pandit of CBS (India) say it will take another 5 or 10 years before Indian performers can make a mark in the West. Tours by Remo and others in the United States have been unsuccessful and frustrating because they do not sing of things familiar to American audiences, Mr. Pandit and others in the industry said.

''It was very frustrating for Remo,'' Mr. Pandit said. ''He was singing about things that didn't appeal to Americans, about flooded streets, bad telephones and delayed flights.''

Some artists are attempting to broaden their appeal. Sharon Prabhakar, an actress and singer who has appeared in the Bombay productions of ''Cabaret'' and ''Evita,'' has begun to sing versions of songs by Madonna and Tracy Chapman in her performances, along with other compositions in English. Increasingly recognized as an innovative artist, Miss Prabhakar acknowledges that ''there has to be an avalanche of good performers if the world is to notice us,''

''That is when the doors will open,'' Miss Prabhakar continued. ''But the factors ranged against us are frightening.''