Teleprompter, the nation's largest cable television company, and Viacom International, a leading syndicator of television programs, yesterday announced that Viacom's pay television subsidiary SHOWTIME will become a joint venture of the two companies beginning next January.

The move significantly raises the ante in SHOWTIME's challenge to Home Box Office, a unit of Time Inc., which is currently the nation's largest pay-cable television network, with nearly 2 million subscribers in over 600 cable systems nationwide.

Teleprompter has wired 1.15 million homes for cable around the country, and currently about 300,000 of these also receive pay television programming. Of this number, 250,000-mainly in New York and Los Angeles - receive HBO.

But under the new joint venture, Teleprompter will cancel its contract with HBO when it expires on jan. 1 and switch these 250,000 homes over to ShOWTIME. Teleprompter will own 50 percent of SHOWTIME. Currently SHOWTIME has only 300,000 subscribers. The joint venture will double this instantly.

Like HBO, SHOWTIEM provides movies and some original live entertainment attractions each month for subscribers. The fee for each system is approximately $10 per household per month, on top of the basic monthly cost for being hooked up to the cable system.

Officials of Viacom and Teleprompter yesterday said the joint Venture would both increase the distribution of SHOWTIME and allow it to produce more original programming in order to win new subscribers.

The dollar size of Teleprompter's investment in SHOWTIME was not disclosed, but the companies said each would own 50 percent of the venture.

"The investment in SHOWTIME markes Teleprompter's entrance into the pay television network distribution business," said Russell Karp, president of Telepromoter. "SHOWTIME, I am confident, will become the leading entity in pay television," he added.

Time Inc., in a statement, said that "While we regret the loss of Telepromoter, which represents about 13 percent of our subscriber base, we remain confident about HBO's continued dramatic growth and penetration performance and about the vitality of the cable television industry."

HBO was started in 1972, and Time reported that it broke into the black in the third quarter of 1977, and has been profitable since then.

HBO has been sending its programming out to affiliated cable systems through satellite transmissions since last March and Now reaches subscribers in about 30 states. It expects to reach all 50 states by January.

Viacom is one of the fastest growing companies in the entire broadcasting industry. It became independent in mid-1971 when it spun off from the cable and syndication arm of CBS Inc. Its main activities involve worldwide syndication of old network television series like the Mary Tyler Moore show, Beverly Hillibillies and Gunsmoke.

It also has distribution rights to about 350 movies. And its produces many of the game shows seen on television in the afternoon and early evening. It also is the sixth largest owner of cable television systems, with over 360,000 subscribers, mainly in California include its cable television system, but on revenues of $58.5 million.

Teleprompter's activities mainly include its cable television system, but it also owns Muzak, and Filmation, a leading supplier of children's programming for Saturday morning time slots.