Yes, the Special Virus Cancer Program (no dash) did exist. It was intended to identify cancer-causing viruses, with the aim of preventing and curing human cancers. It was in some ways a failure, in other ways a success.
It's described in a number of places, including this 1971 article in Science (24 Dec 1971:Vol. 174, Issue 4016, pp. 1306-1311 DOI: 10.1126/science.174.4016.1306):
Special Virus Cancer Program: Travails of a Biological Moonshot
Quoting from that article:
... a uniquely ambitious attempt at targeting basic research toward a
specific goal,the Special Virus Cancer Program (SVCP) of the National
Cancer Institute (NCI). The SVCP, now in its eighth year ... seems to
have come within reach of a major goal, the isolation of viruses
presumed to cause cancer in man. ... The program was launched in
1964, largely on the strength of the association then coming to light
between the African cancer known as Burkitt's lymphoma and the
herpes-type virus named after Epstein and Barr.
To put that in context, in the 1950s and 1960s the discovery of cancer-causing viruses in animals (especially chickens) led many scientists to hypothesize that all cancers, including human cancers, were caused by viruses. If so, then this offered a possible cure or prevention for cancer. This led to world-wide intense research into links between viruses and cancer, of which the SVCP was one research program.
As it turned out, some cancers are caused by viruses, but they are a minority of human cancers. The basic research did turn out to be very useful in understanding how cancers can form and progress, as well as in basic virology, and there has been some progress (the vaccine for human papillomaviruses is an indirect outcome of the program), but overall the hypothesis was wrong, and the overall approach of a massive "moon-shot" program was probably misguided.
Without reading the conspiracy theorist, I assume they're claiming the program was aimed at causing cancer in humans, which is of course 100% backwards.