I am a mathematics postdoc working outside the US and this year I am preparing for applications for positions (mainly in the US). I should also add that I am not a US citizen.
Sometime ago I have seen in the comments to a question here somebody said that tenure track positions are unlikely (though not impossible) to be offered for people working outside USA. I can understand this, since a tenure track position is meant to end in tenure, I mean, I have the impression that universities hire someone with the intention/hope that he/she will be granted tenure eventually.
I am hoping to secure a 2-3 years visiting position in mathematics so that I can introduce myself to the academia in the US, and then maybe apply for tenure track positions. But the question is, whether the same thing is true for these positions. That is, is it hard to get even a visiting position for someone working outside the US?
Also, I have a good command of English and a high TOEFL score. Do you think I should add this to my application package (e.g. mention it in the cover letter, or attach a copy of the test result, or have it sent to the universities etc.) to counter the fact that I am not a native speaker of English?