The headline gives only part of the sentence. The full sentence, as reported in The Guardian, is
“I will say this: if I was an American citizen, I wouldn’t vote for Hillary Clinton if you paid me!”
We can isolate the conditional sentence as
If I was an American citizen, I wouldn’t vote for Hillary Clinton if you paid me.
This is a typical conditional construction which uses the past simple form (here: was) in the if-clause and a modal (here: would in wouldn't vote) to indicate an unreal condition (sometimes called irrealis). Farage is not an American citizen, but this sentence talks about what he would not do if he was an American citizen.
The clause if you paid me is still in irrealis mode since it's in the past tense. Here if means even if.
So, the structure of the headline part of the quote is
I wouldn't do X, (even) if Y happened.
or, the reverse:
(Even) if Y happened, I wouldn't do X.
See also Michael Swan's Practical English Usage 261.10: If, meaning 'even if'
We can use 'if' to mean 'even if'.
I'll finish this job if it takes all night.
I wouldn't marry you if you were the last man in the world.
Except taken from 'if', meaning 'even if'. Why would ommision occur in some cases?