While the rune itself has no direct connection to Nazism, the Sig rune used by Karl Maria Wiligut (Hitler's official occultist) in his own runic row (Wiligut runes) was used in the context of Nazi mysticism and is most commonly used to refer to the insignia of the Schutzstaffel (SS) of the Third Reich.
Guido von List in his "Armanen runes" called the rune "Sig", apparently based on Sigel, thus changing the concept associated with it from "Sun" to "victory" (German Sieg), arriving at a sequence "Sig", "Tyr" in his row, yielding Sigtyr (God of victory), a name of Odin. Under this name of "Sig rune", the s-rune played a certain role in Fascist symbolism, most notably in the badge of the Schutzstaffel (SS), but this is credited to the Wiligut runic row of Karl Maria Wiligut as opposed to Guido von List.
The SS Sig Runes design was created in 1931 when Walter Heck, a Sturmführer in the SS, drew two reversed and inverted Sig Runes side by side and noticed the similarity to the initials of the SS. Heck sold the rights of the Sig Runes to the SS for 2.5 Reichsmarks, and the runes were quickly adopted as the insignia of the Schutzstaffel and became one of the most commonly used forms of SS unit insignia.
The Hitler Youth also used a single Sig Rune, but not as the emblem of its organization. The similarity to the SS insignia was an indication that the Hitler Youth was considered by many to be a central recruiting area for membership in the SS.
The last two letters of the logo for the American rock band KISS resemble the SS symbol. The band had no National Socialist or antisemitic leanings, bass player Gene Simmons being an Israeli-born Jew (guitarist Paul Stanley is also Jewish), and the likelihood is that the similarity is unintentional. The band uses a Kiss Killers Album Cover.jpg of the logo in Germany, where display of the SS symbol is illegal.
The first letter of the logo of American thrash metal band Slayer also bears a resemblance to the Sig rune. Although the band denies any Nazi or antisemitic accusations by the media, they are famous for their song "Angel of Death" which tells the story of Josef Mengele, and others songs inspired by Nazi Germany, like Behind the Crooked Cross or SS-3. Guitarist Jeff Hanneman is also known to be a collector of Nazi Germany memorabilia of all sorts and to have an interest in World War II history in general.
Austrian experimental and martial group Der Blutharsch originally used a logo that consisted of a single Sig Rune. A logo involving oak leaves and an iron cross was later implemented to replace it and all previous usage of the logo was replaced with the new logo, including repressings of old album art.
Scottish punk/new wave band The Skids use the rune in place of the "S" on some of their releases.
Harry Potter has a lightning bolt on his forehead which appears to resemble the rune.