In a way this depends on how you define 'the internet'. If you mean the way you and I are accessing web pages etc. right now then that is probably more of a hypothetical since the Soviets never built something like that and never had a real plan to build one.

If you mean the internet in the sense of a big computer network for sharing information, the USSR had a couple of iterations on the idea. As outlined above the USSR's interest in a world wide web-type construction was limited, but the idea of a network of computers to facilitate economic planning was much more appealing. Logically it follows that any such network, which is a massive undertaking to roll out, would be limited by the techological means available but also by the social and political setting. For yet another 'alternative internet' you might also like to look at Minitel in France.

Anyhow, I won't go into the nitty-gritty of the acronyms for the assorted programs/concepts in the USSR but basically there were two broad ideas for such networks in the USSR. The first major one was promulgated under Khrushchev and envisaged regional computing centres, that local enterprises (as well as design bureaus, scientific institutes etc.) could use to crunch numbers and send information to other actors in the economy. This aligned roughly with Khrushchev's policy around a decentralised, regionalised, economic model with clusters of enterprises is an area being managed by a Sovnarkhoz.

Khrushchev's plan to completely overturn the command/planned economic model (and a bunch of other things) turned out to be so popular he was thrown out of the job in 1964. In the Brezhnev era the idea of another network was put forward, this one aligning with the industrial ministries - each was supposed to build their own network down to the enterprise level, and use that to manage things like reporting of indicators as well as to track inventory (which when you consider that allocation of material was the most common bottleneck in producting, was pretty important). This plan was never completely rejected, but it also never got sufficient traction. This meant that the project wasn't properly funded, the different networks being built by the various bureaucratic actors (the ministries, Gosplan etc.) were not compatible (since no one managed to impose a standard) and hence the information couldn't be shared/utilised for planning the economy. Some of the same problems that plagued the paper-based economic reporting persisted, like enterprises lying about inventory which mucked up planning and statistics.

Some sources, from which you can get much more detail and explore issues like Soviet computers being behind the west in terms of development:

Slava Gerovitch, "InterNyet: why the Soviet Union did not build a nationwide computer network" pdf link

Slava Gerovitch, "From Newspeak to Cyberspeak" - this is moreso about the language and intellectual culture of cyberneticists, but this naturally overlaps with discussions of the Khrushchev era networking project/s.

Martin Cave, "Computers and economic planning: the Soviet experience" - covers more of the later Brezhnev era efforts

There is a fairly new book out called "How Not to Network a Nation: The Uneasy History of the Soviet Internet" by Ben Peters. I haven't had a chance to read that yet, but this podcast with the author goes into a fair bit of detail about OGAS (a later network plan) as well as some of the more far out ideas thought up that didn't take off in the USSR.

Feel free to ask more questions and I'll see what I can dig up.