If Galt and his strikers had a sports team, its logo would definitely be a dollar sign. Their super secret clubhouse, Atlantis, actually has a gigantic dollar sign hanging above it. (We'll let the decorating crowd decide whether or not that's in good taste.) The dollar sign is featured on the cigarettes produced in Atlantis, and it is also the emblem that Dagny scrawls on Nat Taggart's statue as a signal for the strikers to come get her.
Why have Galt and his strikers taken on the dollar sign as their symbol? We'll let Owen Kellogg explain it, since he gets to the point faster than Francisco in his wedding-crashing money speech in Chapter 2.2:
The dollar sign? [It stands] for a great deal. It stands on the vest of every fat, piglike figure in every cartoon, for the purpose of denoting a crook.... It stands – as the money of a free country – for achievement, for success, for ability, for man's creative power – and, precisely for these reasons, it is used as a brand of infamy....It stands for the United States. (188.8.131.52-179)
That is a lot. Dollar signs are an appropriate emblem of Galt's quest and his values because they represent the things his value system prizes: money, capitalism, and America. Money itself is seen as a product of people's hard work and ability, which are also highly prized in Galt's value system. The dollar sign is seen as negative by the looters, so it is fitting that Galt's system, which opposes everything about the looters, would adopt it as a symbol of pride.