The rocket that sent Sputnik 1 into space is the SPUTNIK - PS by the former Soviet Union(now Russia).

r-7

The first Russian rocket was called Sputnik. Sputnik was sent in to space in the year 1957 and returned within 92 days.

Sputnik was the first artificial Earth satellite, sent into orbit by Russia. The long-retired Sputnik rocket that was used to lift off the Sputnik 1, 2, and 3 payloads was an unmanned orbital carrier rocket (8K71PS) from the R-7 family of rockets, similar to America's (also retired) Vanguard and Juno I rockets.

The Explorer but it wasnt a rocket, it was a satellite