I do not see libertarianism as inherently left-wing or right-wing.
It seems to me that the most common way for someone to become a libertarian is through a combination of left-wing instincts and a pro-markets view of economics. This matches my own experience, and while I don't know many other libertarians in person it does not seem to be an uncommon experience.
I believe that it is generally easier to change people's factual beliefs than their instinctive moral beliefs. Given this, I think that the best prospect for recruiting people to the libertarian cause is to bring people over from the left. This is difficult, in that, if I am honest, I do see our position as being closer to that of the right.