Excellent question! Certainly during the Civil War, the Red Star was closely associated with the Bolsheviks, and is preserved even today on Christmas trees across the country, but it has a little longer history.

Stars have long been associated with the Imperial army, since at least the 18th century; here is Alexander Suvorov, with a variety of Prussian and Russian Imperial Orders. The Alexander Nevsky and Saint Vladimir orders are both red, but they are not yet the iconic 'red star' nor are they universal symbols of the Imperial army.

The exact origin of the red star in the Civil War is somewhat obscure, and there are several competing hypotheses.

In 1908 the revolutionary scientist Alexander Bogdanov publishes a utopian novel entitled Red Star, about an ideal communist society on Mars. This book was set during the 1905 Revolution and became quite popular in the lead-up to the 1917 Revolution.

One argument places the origin of the red star symbolism in 1918:

One of the Bolsheviks' first tasks on coming to power was the creation of the new state and its clear differentiation from its predecessor...In early 1918 a red flag with RSFSR on the canton had been introduced, but in mid-1918 this was replaced by a red flag adorned with the hammer and sickle surmounted by a red star. (28)

(Graeme Gill, Symbols and Legitimacy in Soviet Politics)

This same timeline is somewhat fleshed out in another article, which highlights the revolutionary Nikolai Podvoisky.

The red star was not originally in the mandatory array of symbols for the crest of the USSR, as is evidenced by the draft designs submitted in competition. But one did contain a “monogram” (the abbreviation “USSR,” in the upper portion, between ears of grain), which sparked the idea of replacing it with a red five-point star (with no emblem in its center). There is extant a note handwritten by Avel’ Safronovich Enukidze, secretary of the CEC Presidium (the Presidium having delegated to the Secretariat the job of setting up a commission to develop a state flag and crest for the USSR). The note gives a series of recommendations to the artists of Goznak who were designing the crest of the USSR and mentions, among other things, the five-point star: “Above will be placed a five-point star outlined in yellow.” (77-78)

(N.A. Soboleva, From the History of Soviet Political Symbolism, Russian Studies in History)

The red star symbolizes Mars, quite explicitly in Bogdanov's novel, as well as blood and beauty. Other Soviet symbols have clearer origins. The hammer and sickle was the result of a public contest held by Lenin and Lunacharsky, won by the artist Yevgeny Kamzolkin, while L'Internationale was adopted quite readily and preserved until WWII.

There are several apocryphal stories about Trotsky and Lenin designating the red star as a symbol of Bolshevism, but they are not substantiated. Nonetheless by 1918 the Red Star was an important symbol of the Bolsheviks and by the early 1920s it had become central to the new state.